Math Forum - Problem of the Week
Submissions for Bowling Buddies
Student Short Answer Long Answer
Student 1
The final score of the
match was: Cheri at
172, Jake at 151,
Miguel at 112, and
Anita at 94.
Student 2
For my final answer I
had Cheri with 172
points, Jake with 151
points, Miguel with
112 points, and Anita
with 94 points.
I wrote down the information that the problem gave me. I then created a guess and check
table with the columns stating: Anita, Cheri, Miguel, Jake, Total- 529, and Check. I started
with the number for Anita and I subtracted 18 from 97 and got Miguels score of 115. Then I
took the number 97 and doubled it and subtracted 16, getting Cheri's score of 178. Cheri
outscored Jake by 21 so I subtracted 21 from 178 and got Jake's score of 157. I used the
numbers 95, 90, 92, and 93 and I calculated the other scores using those numbers. I then
used the number 94 and figured out that THAT was the number to do my equation with. (x)+
(x-18)+(2x-16)+(2x-16-21)=529.
First I made an equatioin:
Miguel = x
529 points= (x-18)+2(x-18)-16+(2(x-18)-16)-21
after that, i made a guess and check table.
Miguel / Anita / Cheri / Jake / Check(529)
__________________________________________
50 / 32 / 48 / 27 / 157 (too low)
100 / 82 / 148 / 127 / 457 (too low)
110 / 92 / 168 / 147 / 517 (too low)
112 / 94 / 172 / 151 / 529 *correct*
Student 3
I think i scored
thehighest in the
bowling game
eye do knot think eye
should answer this
kwestion
The reason for that is because when i go bowling i alwayz get the
highest score
Student 5
boys 5 and the girls 6
because my mom doesnt allow me 2 go bowling and i do not wish to
disobey her orders cause she always threatens 2 send me on the first
banana boat back 2 africa and im tired of fighting for my food
everynight.
i dont know how i got it
Student 6
The answer to the
I found my answer by using algebra. By using equations I created for
Student 4
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 1 of 24
problem is that the
girls outscored the
guys by 3 points.
Student 7
The final score for the
boys was 263 and for
the girls it was 266.
Student 8
The girls score was 274
and the boys score was
255. So,the girls won
by 19 points.
Student 9
The girls score was 266
and the boys score was
263. So,the girls won
by 3 points.
© 1994-2016 Drexel University
http://mathforum.org/pows/
all the bowlers, I could find the answer more easily. I combined
some equations together to find the total points a specific bowler
had. Then I checked to see if my answer was right, I added all the
points and got 529. The final score of the match was really close.
The girls outscored the guys by 3 points. So, the girls had beaten
the guys by 3 points.
What i did was i guessed and check. I decided to start of with
miguel and used numbers around 100. I guessed 110 and then i
subtracted 18 to receive Anita's score and got 92.Then i multiplied
92 by 2 and subtracted 16 my answer is now 168 for cheri. then i
subtracted 21 from 168 i was left with 147. I added all my numbers
up and my answer was 517 which is not right.
Then i decide to try 112 for miguel and i subtracted 18 to get
anita's score and i got 94. Then i multipplied 94 by 2 and
subtracted 16 and got 172 . I then subtracted 21 to receive jake's
score which is 151. I added 112 and 151 and i got 263 for the boys
score and i added 94 and 172 to get the girls score wich is 266.
I used an equation with variables to solve the problem. x+x-18+2x20+2x-57=529 We got 6x-95=529, so I added 95 to both sides and got
6x=624. Then I divided both sides by 6 and got x=104. So I knew
that miguel was just x, Anitas was x-18, Cheris was 2x-20. The wat
I got 20 was because I did 2(x-18)-16=2x-36-16=2x-20, and jakes
score is 2x-57.so now all i did was plug in 104 for x.in all the
equations so miguel has 104 points, anita has 86 points, cheri has
188 points, and jake has 151 point.and when you add them all up
together you get 529.
I used an equation with variables to solve the problem. x+x-18+2x-52
+2x-73=529 We got 6x-143=529, so I added 143 to both sides and got
6x=672. Then I divided both sides by 6 and got x=112. So I knew
that miguel was just x, Anitas was x-18, Cheris was 2x-52. The way
I got -52 was because I did 2(x-18)-16=2x-36-16=2x-52, and jakes
score is 2x-73. So now all i did was plug in 104 for x, in all the
equations. So miguel has 112 points, anita has 94 points, cheri has
172 points, and jake has 151 point, and when you add them all up
together you get 529.
Miguel=x=112
112
Anita=x-18=94
+ 94
Cheri=2x-52=172 +172
Jake=2x-73=151
+151=529
Page 2 of 24
Student 10
the final score of the
match is girls:266 and
boys:263
Student 11
down
Student 12
The final score of the
match was that Anita
had 94, Miguel had
112, Cheri bowled 172
points, and Jake
bowled 151 and the
© 1994-2016 Drexel University
http://mathforum.org/pows/
i guess and check so i added boy's score miguel got112 and jake got
151 i added both and i got 263 which is the final score for the boys,
anita got 94 and heri got 172 i added both and i got 266 and these
are the final scores for each team,and of course the girls won the
game.
Let...
a = anita
c = cheri
m = miquel
j = jake
m-a = 18 --------> m-a = 18
2a -16 = c
-m
-m
c+21 = j
-a = -m + 18
(-a) -1 = (-m+18) -1
a = m -18
***a = m-18***
2a -16 = c ---------> 2(m-18) -16 = c
2m - 36 - 16 = c
2m -52 = c
***c = 2m-52***
c + 21 = j ----------> 2m-52 +21 = j
2m -31 = j
***j = 2m -31***
j = 2m - 31
-2m -2m
-2m+j = -31
-j -j
-2m = -j -31
-1(-2m) = -1 (-j -31)
2m = j + 31
____ _____
2
2
The method that we used to get the answer for this problem is guess
and check. First we decided to use 100 for Anita's score since it
seemed like you could get everyone else's score from hers and that
she had the lowest score from what we could tell. Since we guessed
that she had 100 Miguel had to have 118, Cheri had to have 184, and
Jake had to have 163. Those all fit the first descriptions, but not
Page 3 of 24
girls outscored the
boys by 3.
Student 13
Student 14
Student 15
Girls scored three
more points than the
boys, becuase ( 529
dived by 4 equals (n)
which is the total score
of the match)
The girls would win
with a score of 266.
The boys score is 263
The girls win by 3
points 266 to 263.
© 1994-2016 Drexel University
http://mathforum.org/pows/
the last one which was "the total scored by all four kids was 529".
We got this wrong, because when we added our answers up we got 565.
As you can tell the answers do not match up, but we used our mistake
to come up with an answer that was correct. We subtracted our total
from their total and we got 36. So we knew that our answer was 36
off and that we had to figure out numbers to take away from the kids
numbers to make it 36. We knew not to do 9 (because there are four
of them that would be anybody's first guess), because Anita's
compared to Cheri's had to be doubled. Then comparing Cheri to Jake,
we had to have his doubled too. We looked at it and since Cheri and
Jake's had to be doubled we knew that every 1 we subtracted or added
from Miguel and Anita we had to add or subtract 2 from Jake and
Cheri. We added all of those up (1+1+2+2) and we got 6. Then we
divided the 36 by the 6 and we got 6. So then we knew we had to take
6 or 12 from each one. We subtracted 6 from Miguel and got 112, we
subtracted 6 from Anita and got 94, we subtracted 12 from Cheri and
got 172, and we subtracted 12 from Jake and we got 151. We only
subtracted, because the number we got before (565) was too high.
When we ended up with 529 our work was not complete for we had not
got the difference between the boys (Miguel and Jake) and the girls
(Anita and Cheri), so we added both of theirs up seperately. For the
boys we got 263 and for the girls we got 266. THEN we knew our
answer was complete.
529 dived by four equals 132.25, then minus 18, then 20,then
multiplied by 21 would equal 529.
I used 4 variables: A,C,M, and J to represent the scores of the
individuals. The information allowed me to create the following
equations. A=M-18, C=2A-16, C=J+21, C+A+M+J=529
Substituting into the final equation allows me to solve for one
variable, I chose to solve for M. Substitution gives me: 6M-143=529,
and therefore M=112. This allows me to say that A=94, C=172, and
finally J=151. This gives us the boys' score as M+J=263 and the
girls' score as A+C=266. The girls win.
What I did was make a variable and then make expressions for each
person. Everybody is based off of Anita, so I made her our variable
of
Page 4 of 24
x. so
x = anita
from this I could make an expression for miguel. You know that
miguel is 18 more than anita, he is 18 more than x or, x + 18
so there for
miguel = x + 18
Now cheri is 16 less than 2 times anita or x
2x is equivalent to 2 times x and 16 less than 2x is equivalent to
(2x - 16) so there for
cheri = 2x - 16
jake is 21 less than cheri so that is that same as 2x - 16 - 21
if you simplify that you get 2x - 37 so
jake = 2x - 37
so the four expressions you have are
x = anita
x + 18 = miguel
2x - 16 = cheri
2x - 37 = jake
now you know that all of these scores added together equal 529 so you
can set up an equation adding allll of those expressions together:
x + x + 18 + 2x - 16 + 2x - 37 = 529
you can then simplify it into
6x - 35 = 529
now we solve for x:
6x = 564
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 5 of 24
x = 94
Now we know Anita's score was 94.
All we have to do is substitute 94 for x in all of the other
expressions and we find our answer
94 + 18 = miguel
112 = miguel
2(94) - 16 = cheri
188 - 16 = cheri
172 = cheri
188 - 37 = jake
151 = jake
now just to find out the final score we add up the 2 boys:
112 + 151 = 263 = boys score and
94 + 172 = 266 = girls
so the girls won by 3 points
the final score was 266-263
reflection
this algpow was pretty simple all that you had to do was make up
expressions for each person and then solve I didnt really find
anything tricky about it, but it was a nice problem altogether, and
good practice I didnt have any difficulties and solved it rather
quickly but it was still fun
Student 16
Anita scored 94, Cheri
scored 172, Miguel
scored 112 and Jake
© 1994-2016 Drexel University
http://mathforum.org/pows/
Need to solve C+J+A+M=529
From the problem we get:
A=M-18
Page 6 of 24
scored 151. Then for
girls versus boys, the
girls win by 3 points.
Student 17
df
Student 18
163+145+121+100=52
9
Student 19
therefore, that is the
answer.
C=2A-16
C=J+21
Since C is a more common thing we'll make each other person's
equation in terms of C.
Therefore we get
A=(C+16)/2
M=(C+16)/2+18
J=C-21
C=C
Substituting will give us:
C+(C-21)+(C+16)/2+[(C+16)/2+18]=529
Combining gives us 3C+13=529 where C=172. Filling this into the
other equations gives us the below answers. Anita scored 94, Cheri
scored 172, Miguel scored 112 and Jake scored 151.
Then for girls versus boys we get 266 G versus 263 B. Girls win!
dfadf
I found my answer by useing a table. I made shour thatAnita and
Miguel was 18 numbers apart. The I made shour that Cheri andJake was
21 numbers apart. Then if those numbers were correct. I added all
the numbers to see if they equal to 529 and if they were then iI was
correct.
How I got my answer was by getting a first reseble number
to give me cheri`s answer and to get jake answer.
Anita number was 94
Miguel number was 112
Cheri`s number was 172
Jake number was 151
Student 20
If the total scored by
all four kids was 592,
the final score for Jake
was 151, Anita 94,
Cheri 172, and Miguel
112.
Total 529
To begin this problem, I wrote down the formulas to help me find the
solution. The formulas I came up with are the folowing.
Jake's score= C-21=J
Anita's score= M-18=A
Cheri's score= (A*2)-16=c
Miguel's score= M
By looking at the formulas, I noticed that I had to find Miguel's
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 7 of 24
Student 21
Student 22
The final score of the
match was: girls 266,
boys 263.
Anita’s score is 94,
Cheri’s score is 172,
Miguel’s score is 112,
and Jake’s score is 151
score. I plugged in 100 and after I did the math I found that the
final score was 450. The next number I tried was 105, again I did the
math and came out with 487. Next, I tried putting in 111 as Miguel's
and came out with 523. That was really close so I tried 112. I found
that that was the correct answer for Miguel's score. With that score
I could complete the rest of the formulas and found my answers were
correct.
1. First I used "M" to indicate Miguel's score. Then I will write
everyone elses score as a function of "M".
2. Anita's score as a function of "M" is: M-18
3. Cheri's score was: 2(M-18)-16 or 2M-36-16
4. Jakes score was: 2M-36-16-21
5. So the equation for the entire score was: M+M-18+2M-36-16+2M-3616-21=529
6. Simplifying the equation: 6M-143=529.
7. Add 143 to each side of the equation: 6M=672.
8. Divide both sides by 6: M=112.
9. Miguel's score is 112, Anita's score is 94, Cheri's score is 172,
and Jake's score is 151. ( You can test by adding the numbers up and
seeing that they equal 529).
10. Add the boys scores to get 263 and add the girls scores to get
266. So the Girls win.
To check my work I went throught it many different times. If I got
an answer that was different from the rest I would see how I got it.
For bowling buddies it took me a while to find out a logical way to
figure this problem but with some help from an Algebra learning book
and some input from my dad I got this P.O.W done. I found out I could
use algebra and eliminate the variables till I only had one, like
making everything according to C as one of my variables and then I
could find out what C is and then know what every other variable is.
So to start I put down the information they gave me using variables.
A=M-18
C= 2A -16
C=J+21
The total score of the four bowlers added up together is 529
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 8 of 24
529=A+M+C+J
I translated everyone’s scores relative to Cheri’s, or C, I started
with Jakes and eliminated the variables till C was left.
C=J+21
C-21=J+21-21
C21=J
J=C-21
(C-21)
C=2A-16
C+16=2A-16+16
½(C+16)=(2A) ½
½ C+8=A
A=½ C+8
A=M-18
A+18=M-18=18
A+18=M
M=A+18
M=(½C+8)+18
M=½ C+8+18
M=½C+26
C-21
529= A+M+C+
529= (½ C+8)+M+C+C-21
529= ½ C+8+(½C+26)+C+
529= ½C+8+½C+26+C+ C-21
Now I only have one variable so I can now find out Cheri’s bowling
score by subtracting 13 from 529 and then dividing 516 by 3 because
that is how many times Cheri’s score went into 516
529=3C+13
529-13=3C+13-13
516=3C
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 9 of 24
C=516/3
C=172
Once I fond out what Cheri’s score was I could use the formulas I
created earlier to figure our every one else’s scores.
J=C-21
J=172-21
A=½C+8 A=½ (172)+8
M=½C+26
M=½(172)+26
J=151
A=94
M=112
Anita’s score is 94, Cheri’s score is 172, Miguel’s score is 112, and
Jake’s score is 151
Student 23
The score for the girls
was 266, and the score
for the boys was 263.
It was fun to learn some more algebra and it did take a while to
complete but it was fun.
First we used the paragraph below to make a list that is easier to comprehend.
Anita scored 18 less than Miguel. Cheri's score was 16 less than twice Anita's. Cheri
outscored Jake by 21.
We turned the paragraph into this.
Anita = m (Miguel) - 18
Cheri = ((m - 18) * 2) - 16
Miguel = m
Jake = c (Cheri) - 21
After that, we did the math from the list above to simplify the problem. For Cheri, we did
the following steps:
((m - 18) * 2) - 16
18 * 2 = 36
m * 2 = 2m
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 10 of 24
Therefore, a simplified version of the problem would be:
2m - 36 - 16
After that, we took the 2m off temporarily, so the problem looked like this:
-36 + -16 = -52
Adding the 2m back on, Cheri's score would be simplified to 2m - 52. Next was Jake. We
did the following:
c - 21 = Jake
Since Cheri's score was 2m - 52, Jake would be 2m - 52 - 21.
Doing the same mathematical process as for Cheri, we ended up with this as Jake's score:
2m - 73
That left the chart looking like this:
Anita = m - 18
Cheri = 2m - 52
Miguel = m
Jake = 2m - 73.
Sice we knew that the total of the scores was 529, we laid out the scores like one very long
problem.
(m - 18) + (2m - 52) + m + (2m - 73) = 529
Now we slowly started to do the problem, our goal to find m. We eventually got it down to
this:
6m - 143 = 529
Next we looked at it like a pan-balance problem. To get rid of the -143, we added 143 to
both sides.
6m = 672
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 11 of 24
Then we divided by 6.
m = 112
From there, we could figure out the rest of the scores! Here were the final scores:
Anita = 112 - 18 = 94
Cheri = (112 - 18) * 2) - 16 = 172
Miguel = 112
Jake = 172 - 21 = 151
To finish the problem, we added the girls' scores and the boys' scores together.
Girls = 266
Boys = 263
Student 24
The girls won, 266 to
263.
© 1994-2016 Drexel University
http://mathforum.org/pows/
The last step was to check our math. Fortunately, 266 + 263 = 529.
First I made all of the names into four variables, a, m, c, j. Then
I wrote out all of the equations.
m-18=a
a*2-16=j
j+21=c
Then, i broke that down to
a=m-18
m=a+18
c=j+21
j=c-21
Then, I divided them into teams
girls=a+c=(m-18)+(j+21)
boys=m+j=(a+18)+(c-21)
Then i simplified that to
a+c=(m+j)-18+21
m+j=(a+c)+18-21
And that simplifies to
a+c=m+j+3
m+j=a+c-3
Now, I divided 529 by 2 and got 264.5. And since the boys and girls
teams diference was three, i added half of three to this to get the
girls score, and subtracted half of three to get the boys score.
Page 12 of 24
Student 25
In the end i found out
that Anita scored 94,
Miguel scored 112,
Cheri scored 172, and
Jake scored 151.
This problem asked me to find the score for each bowler. It gave me
hints on what the score was for each player by comparing two kids
scores.
First i wrote down the comparison of two kids in algebraic form.
Here they are
A=m-18
C=2A-16
J=C-21
They also gave what the total score is:
A+M+C+J=529,
I substituted A for every variable (M, C, J) so I only had to solve
one variable. I know that A=m-18 so to get them in terms of A I
added 18 to each side, and i had M=A+18.
Cheri’s score, C is already given in terms of A. C=2A-16.
For J =C-21. Since we know C=2A-16 we can say J=21-16-21. So once w
put all the variables in terms of A we filled the equation
A+C+J+M=529
6A -35=529
6A=564
6/564= 94
To find out the other kids scores I finished each equation knowing
that. C=188-16=172
J=172-21=151
M=112
A=112
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 13 of 24
Student 26
The girls scored 266.
The boys scored 263 in
the bowling
tournament. The girls
won the bowling
game.
> To figure this problem I need to find out what Miguel's score is to
> find out Anita's, Cheri's, and Jake's score.
> I started out with a quick chart that shous the equation for each
> person.
> I am going to use m for Miguel for my variable. I am also going to
> use c for Cheri.
> Person ^ Equation
---------^----------------------------> Anita ^ m - 18
---------^----------------------------> Cheri ^ 2 * (m - 18) - 16
---------^----------------------------> Miguel ^ m
---------^----------------------------> Jake ^ c -21 2m - 52 - 21
---------^----------------------------> total ^ 529
> Cheri's box can be made smaller to do that I did this.
> 2m - 36 + 16 I got 36 by multiplying 2 * 18. I add what I can which
> is 36 and 16.
> 36
> +16
>----> 52
> Now the chart changes to this.
> Person ^ Equation
---------^----------------------------© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 14 of 24
> Anita ^ m - 18
---------^----------------------------> Cheri ^ 2m - 52
---------^----------------------------> Miguel ^ m
---------^----------------------------> Jake ^ c -21 2m - 52 - 21
---------^----------------------------> total ^ 529
> As you can see Jake's box is a little overboard to. I can size that
> up by taking c - 21 away because c = Cheri's, Cheri's is 2m-52 you
> can replace c - 21 with 2m - 52. So now it will look like this.
> It changes to 73 becasue if you add 52 and 21 together you get 73.
it is just so the equation is shorter. 52 + 21 = 73
> Person ^ Equation
---------^----------------------------> Anita ^ m - 18
---------^----------------------------> Cheri ^ 2m - 52
---------^----------------------------> Miguel ^ m
---------^----------------------------> Jake ^ 2m - 73
---------^----------------------------> total ^ 529
> we know that 529 is the answer because it was given information.
> If you write out Anita, Cheri, Miguel, and Jake's equation out
> together you get this problem.
> m - 18 + 2m - 52 + m + 2m - 73 = 529
> I found out home many m's there are which there are 1-2-3-4-5-6.
> There are 6 total m's.
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 15 of 24
> Then add all of the numbers together.
> 18
> +52
----> 70 Then add 70 and 73
> +73
----143
> The new equation 6m - 143 = 529
> I still do not know what 6m is so add the total 529 and 143 together
> and get 672.
> Now 6m = 672
> The last step in algebra is to divide. The only number to divide by
> 6.
> ___
> 6/672
> The answer is 112.
> 112 = m
> Now you have to plug m "112" to every m that is in the chart.
> Person ^ Equation
---------^----------------------------> Anita ^ 112 - 18
---------^----------------------------> Cheri ^ 2 * 112 - 52
---------^----------------------------> Miguel ^ 112
---------^----------------------------> Jake ^ 2 * 112 - 73
---------^----------------------------> total ^ 529
> 112
> - 18
-------> 94 Anita
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 16 of 24
> 112
> * 2
-------> 224
> - 52
-------172 Cheri
> m = 112 Miguel
> 112
> * 2
-------> 224
> - 73
-------151 Jake
> Then you have to add the girls together and the boys together
because they were against each other.
> 172
151
> + 94
+112
--------------> 266 Girls
263 Boys
> So it ends up that the boys lose the bowling game to the girls by 3
> points.
Student 27
The girls had 266 and
the boys had 263 so
the girls won.
© 1994-2016 Drexel University
http://mathforum.org/pows/
> Tis problem was challenging for me. It understood once I looked
> over it again after my teacher helped me out. I'm still waiting for
> problem that I can figure out all by my self.
To get the answer I started by changing their names into variables that were their initial.
Then, I got to work. First I layed it out: A=M-18 C=2*(M-18)-16 M=M and J=C-21. After
that, I wanted M to be my main variable, so I got everthing to only have a variable of M. Here
is how I did it. Anita's problem was alright so I skiped her. Next was Cheri. On Cheri I just
added the numbers together and got C=2M-52. On Jake, I just subtracted Cheri's score by 21
and got J=2M-73. Then, I layed it out again. A=M-18 C=2M-52 M=M and J=2M-73. From
there, I turned it into a algebra problem to get Miguel's score: 6M-18-52-73=529 And the
answer is M=112. After getting that information, I used it to get the other scores: A=94
M=112 C=172 and J=151. Then I added the numbers up: A+C=266 and M+J=263 which is
Page 17 of 24
Student 28
Anita had 94 points,
Cheri had 172 points,
Miguel had 112 points,
and Jake had 151
points. The boys had
263 points and the
girls had 266 points.
Student 29
Boys had 263 and girls
had 266.
Student 30
The answer is that
Anita scored 94, Cheri
scored 172, Miguel
scored 112, and Jake
scored 151. The girls
beat the boys 266-243.
Student 31
The final score of the
match was, Girls:266
and Boys:263.
my answer.
First, I made each persons clue into an algebraic expression. I used the variable m as a
common variable for Miguel because Migual is the basis of each expression. The expressions
were, Anita= M-18, Cheri=2m-52, Miguel=m, and Jake=2m-73. I then made one big
equation to find what m equals. It is shown on the attached page. I then added up all of my
ms and got 6m. And then I added up all of my regular numbers and got -143. The pan
balance would be 6m and -143=529. To get rid of the negative numbers, I added 143 to
both of the regular numbers. -143 becomes nothing and 529 becomes 672. Now to get m I
divided 672/6=112. That means Migual got 112 points. To find Anita, I did 112-18=94. To
get Cheri, I did (2*112)-52=172. Lastly, to get Jake I did (2*112)-73=151. Finally, to get the
boys score and the girls score, I added all of the boys scores and all of the girls scores. To
check my work, I added everyone's scores together to make sure it equaled 529.
What I did fo this POW was make a chart of all the names and used the
guess and check strategy. The person that I started the scores with
was Anita, because after looking at the clues, I could tell she
probably had the lowest score. On the 4th try, when I put 94 fo
Anita, I used the equations to get 172 for Cheri, 151 for Jake, and
112 for Miguel. After I did that I added up the boys and girls and
got 263 for the boys and 266 for the girls.
I first set up an equation representing every statement said in the
problem, A+M+C+J=529, A=M-18, C=2A-16, ans J=C-21. I then plugged the
problems into the first equation to get 529=(M-18)+M+(2A-16)+(C-21).
Next I put in all the different variables on the left side of the
problem into M to get 529=M+(M-18)+(2(M-16)-16)+((2(M-16)-16)-21). I
then combined like terms to get 529=6M-143. I got M by itself to find
that Miguel scored 112. Then I plugged the 112 into the other small
equations to find that Anita scored 94, Cheri scored 172, and Jake
scored 151. Then I finally combined the boys and the girls scores to
find that the girls beat the boys 266-243.
For this problem, we started with Anita's score. We guessed that
her score was between 90 and 100. We finally got a winner with
Anita's score being 94. We figured out all of the other scores
based off of Anita's. From there, we calculated Miguel's score.
His score was 112 because he scored 16 more than Anita. Then we
found out Cheri's score to be 172 (go Cheri)! Cheri's score was 16
less than twice Anita's. Jake's score was 151 because Cheri out
scored him by 21. These are the scores.
Anita:94
Cheri:172
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 18 of 24
Miguel:112
Jake:151
The girls won by 3 points. You go girls!!!
Student 32
All four scores total did
not add up to 529, it
was 200 less, it was
329 points.
Student 33
The final score of the
match was 263 for the
boys and 266 for the
girls.
Student 34
The final score for the
game is 266 (girls) to
263 (boys).
© 1994-2016 Drexel University
http://mathforum.org/pows/
To find the answer to this pow i first read the problem a lot. i
then set up equations to what i needed to find.
Anita = miguels score -18
Cheri = 18- miguels score * 2 -16
Jake = Cheri's score -21
i began to guess at miguels score, because if i knew miguels score i
would then know anitas score, and i could then find out all of the
other scores. so i started thinking about bowling, and the scores
you get when you bowl. and i started to pulg in numbers, i used the
guess and check method. I started at 100 and worked my way up, i got
to 112 and i plugged it all in with the exuations i made.
Anita :112 - 18= 94
Cheri :112 -18 * 2= 188 -16 = 172
Jake :172-21= 163
Miguel: 112
i then added up all the totals of the scores and got 329
so no, the scores did not match up to 529.
This week's POW asked me to find the final score of a bowling
match using only a series of clues and a total of all the four
bowlers' scores. First I arranged an equation for each of the scores
except Miguel's. They were A=M-18, C=2A-16, J=C-21, in which the
letters stood for each bowler's score. After this I arranged each of
the equations again to include only Miguel's score as a variable.
Then I put every equation and a M on one side in one long equation
and with the total of all scores on the other side. Then I solved
for M and got 112. I plugged this back into the other equations and
got the scores, which were A=94, C=172, and J=151. Finally I added
the boys scores and girls scores to get my answer. That is my
explanation for this week's POW.
The kids bowling are Anita (A), Cheri (C), Miguel (M), and Jake (J).
According to the information given, there can be several equations
made to help answer the problem.
Page 19 of 24
A + C + M + J = 529
A + 18 = M
C + 16 = 2A
C = J + 21
Our goal is to find each kid's individual score to add them up for
each team. The best way to do that is substitute the variables into
the first equation. I'll start with C. With that, it can easily go
to A + C + M + (C - 21) = 529 because of the last equation. The
variable M has two steps to turn it into terms of C. The first step
is to change it into terms of A, which goes A + C + (A + 18) + (C 21) = 529. The next step of turning A into terms of C is tricky. The
way to do that is C/2 + 8 + C + C/2 + 8 + 18 + C - 21 = 529.
The next step to finding the value of C is to make it go to one side
and the other number to the other side. If everything on the left
side of the equation were to be added together, it would look like
3C + 13 = 529. When the 13 is subtracted, the equation looks like 3C
= 516, and when the 3 from the C is divided, C = 172. So, somehow,
Cheri got 172.
Student 35
unknown
If 172 were to replaced in the first equation, it would be A + 172 +
M + J = 529, which is A + M + J = 357. Now it's fairly simple to
find out the other variables. In the last equation, C can be
replaced to make 172 = J + 21, which makes J = 151. In the third
equation, also, it's 172 + 16 = 2A. That is equal to 188 = 2A, or A
= 94. In A + 18 = M, we know what A is, so that makes it 94 + 18 =
M, or M = 112. Now we know everyone's score. We just add A and C
together to get 172 + 94, or 266 as a score. M + J is equal to 151 +
112 or 263. So that's it.
asdflajs;dlfak
Student 36
the final match was 4
u just subtract all the given numbers
Student 37
The final score was
Girls: 266, Boys: 263.
The first thing I did was set one of the people to X, which was
Miguel. I then gave all of the kids an equation. First, Anita was
equal to X-18, since her score was 18 less than miguel. Next, Cheri
was equal to 2(X-18)-16, since her score was 16 less than twice
Anita's. Lastly, Jake was equal to 2(X-18)-16-21, since Cheri
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 20 of 24
Student 38
The final score of the
match was boys 272 to
girls 266.
Student 39
Anita got 106, Cherri
got 206, Jake got 185,
and Miguel got 124.
© 1994-2016 Drexel University
http://mathforum.org/pows/
outscored him by 21. I then, added all of the equations and X
together and got 6X-143. I set the result equal to 529 and solved for
X to find Miguels score. It happened to be 112. Next, I plugged 112
in for X in all of the equations to find the other scores. Anita's
was 94, Cheri's was 172, Jake's was 151. I then added Miguel's and
Jake's scores, which was 112 and 151, to find their total score and
got 263. Next, I added Cheri's and Anita's scores, 172 and 94, to
find their total score and got 266. This means that the Girls won 266
to 263.
For 'Bowling Buddies' I first made an equation to find out how
many points each person scored. I made Miguel's score x. The equation
was x+(x-18)+[2(x-18)-16]+[2(x-18)-16]-21=529. My next step was
solving the equation so I get Miguel's score. Miguel's score was 112.
Then, I found out the score all the other players got. Anita's score
was 94 since her score was 18 less than Miguel. Cheri's score was 172
since her score was 16 less than twice Anita's. Last but not least,
Jake's score was 151 because Cheri had 21 more than him. Finally, I
added up the boys' score and girls' score to get 272 for the boys and
266 for the girls.
To figure out this problem, I started out by giving each person a
variable. The variable was the beginning of each person's name.
Then, I set up the equation 529 = M-18 [2(M-18)-16] + J + M. 529 was
the final score. M -18 was Anita's score, The middle term [2(M-18)16] was Cherri's score. I set this up based on the information I was
told. And J and M were just the regular scores for Jake and Miguel.
To start out simplifying this problem, I simplified the middle term.
Then, the equation was 529 = M-18 + 2M -18-16+J+M. After that, I
combined the three numbers in the equation. That simplified the
equation down to 529=M-52=2M + J+M. Then, I combined all of the M
values to get 529=M-52 + J. Then, I solved that equation by adding
52 to both sides. That gave me 681=4M+J. Since there were to
variables in the equation, I further simplied that out by using
Cherri's equation and subtracting 21 because she outscored Jake by
21. Then, I figured out that equation nd the final simplified term
was J=124.85. So, I rounded that up to 125. Now that I had the value
for M, I could just used put in the different equation values to
figure out the rest of the scores. To figure out Anita, I used the
equation M-18 because Anita scored 18 less than Miguel. That gave me
106. For Cherri, I used the equation 2A-16=C. I put in 106 for A and
that gave me 206 as a final score for Cherri. Lastly, to figure out
Page 21 of 24
Student 40
Student 41
The final score was
266 for the girls, and
for the boys 263.
The final scores of the
match was as follows:
Anita had a score of
119, Cheri had a score
of 121, Jake had a
score of 142, and
Miguel had a score of
137. Therefore, the
boys won.
Student 42
Miguel had 112 points,
Anita had 94 points,
Cheri had 172 points
and Jake had 151.
Student 43
Anita has a score of 94,
Miguel has a score of
112, Cheri has 172,
© 1994-2016 Drexel University
http://mathforum.org/pows/
Jake's score, I used the equation C - 21 because Cherri, or C, got
21 points higher than Jake. This gave me a score of 185 for Jake.
I tried to set up several equations to figure this problem out but
ended up guessing and checking to figure out the answer. sorry about
that mr. p
I did this problem using many steps. First I assigned lables.
Miguels score was M, Jakes score was J, Cheri's score was C, and
Anita's score was A. Then I made equations according to the problem.
The equations were A=M-18, J=C+21, C=2A-16, and A+C+J+M=529. Then I
substituted the equations into the problems, one by one. First I
substituted Jakes equation, and I ended up with A+2C+M=508. Then,
with Anitas equation, I figured out an equation for Miguel. It was
M=A+18, and when i substituted this into the equation, I got the
eqation 2A+2C=480. Then I found another equation for Cheri. I found
it by using Jakes equation. It was C=j-21. WHen I substituted this
into the last equation, which was 2A+2C=480, I got 2A=238, and from
that I got A=119, so Anita's score was 119. I substituted this into
Anitas second equation, which I derived from Cheri's first equation,
and got C=121. Therefore, Cheri's score was 121. I did the same
things for Miguel and Jake, but I used their original equations. By
doing this, I found that Jake got a score of 142, and Miguel got a
score of 137. Jakes score was the highest boy score and Cheri's was
the highest girl score, and Cheris score was lower than Jakes, so
the boys were the winners. That was how I did the POW.
In this week's problem of the week, you have to find the score of
the all the kids from bowling. The clues you get to figure this out,
is Anita's score was 18 les than Miguels, Cheri's was 16 less then
twice Anita's and Cheri outscored Jake by 21. Also, the total of all
four kids was 529. To start out with this problem of the week, I
frist started guessing numbers. I guessed that Miguels score was
100, and figured out the rest's. When I added all of the scores
together, it wasn't high enough, so I had to try a higher score. I
then tried 115. I figured it all out, and once again added them all
up. This time I got a number that was just a little over 529. I then
tried 113, which wasn't right, and that left me to try 112. I
plugged in 112 for Miguels score, and added 112+94+172+151 and the
answer I got was 529, so I knew I had all the scores right.
In this weeks POW I had to find the scores in bowling for 3 friends,
with the total of their scores being 529 and certain restrictions of
their scores, like how Anita's score was 18 less than Miguel, Cheri's
Page 22 of 24
and Jake has a score of
151, the final score
was 263(boys)to
266(girls)
Student 44
girls won 266 to 263
Student 45
Girls= 266, Boys=263
Student 46
The final score was the
girls had the score of
© 1994-2016 Drexel University
http://mathforum.org/pows/
score was 16 less than twice Anita's, and Cheri's score was 21 more
than Jake. Using this I realized that the entire problem was dependent
on Anita's score so I used a guess-and-check method to find the
answer. I first used an even 50 (as Anita's score) in my problem but
came up too short, so then I used 125, but I came up too large, so I
then used 100 and worked my way down, until I found that if Anita's
score was 94, then everyone else's scores when added to each other
would total 529. using this I deducted that Miguel had a score of 112,
Cheri had 172, and Jake had 151. using these numbers I found that the
final score was boys with 263 lost to the girls with 266.
I started this pow by making a simple equation for each of the
people. I noticed that I had to guess and check to get all of the
answers. The best sorce of guessing was to guess Anita's score. My
first guess was 90. After working through the math and solving out
the equations. The toatle score of the kids was 505. This was very
close and I had to go higher since my guess came up short. I decided
that 95 would be a good guess. After solving it down, the totals
came out to be 535. This was much closer than before and I decided
that 94 would be a smart guess. Once I added 18 to get Miguels
score, multiplied by 2 and subtracted by 16 to get Cheri, and
subtract 21 from Cheri to get Jakes score, I came up with the
totals. The total score was 529. Once I added the girls and boys
score the girls won 266 to 263.
I solved this problem by making a simple equation. I based X on
Anita's score, and after that I compared Everybody elses score to X
for example, Miguel score 18 more than Anita did so Migeul= x+18.
So in the end all i had to do was solve for X, and write in
everybody's score compared to X. Here is my work:
x+x+18+2x-16+2x-16-21=529
6x-35=529
6x=564
x=94
Aneta=94
Miguel=112
Cheri= 172
Jake=151
Girls=266
Boys=263
I found this answer by putting an equation together for each kid.
Anita's equation was M or Miguels score minus 18. Cheri's was Anita's
Page 23 of 24
266 to the guys score
of 263.
Student 47
asdfas
score times 2 minus 16. Then Miguels equation was Anita's plus 18.
Finally Jake's was Cheri's minus 21. I finally did a guess and check
and chose the number 108, 120, 110, 114. Finally my last check was
112 I plugged this number in for Miguels. I found Anita's was 94,
Cheri's was 172, Jake's was 151. I then added 94 to 172 and got 266.
Lastly I added 151 to 112 and got 263. Resulting in the girls winning
by 3 points.
fasdfasfasdf
© 1994-2009 Drexel University
http://mathforum.org/pows/
© 1994-2016 Drexel University
http://mathforum.org/pows/
Page 24 of 24