Math Forum - Problem of the Week
Submissions for Boxes of Cereal
Student Short Answer Long Answer
Student 1
They both have a third
of a box left after five
days.
Student 2
Each Child had 0 left in
their box.
Student 3
Lily and Mikey both
had 1/3 of their boxes
left.
Student 4
Each child had 1/3 of
the cereal box left.
On Monday Lisa's box has 30 out of 30 parts while Mikey's has 15 out
of 30. On Tuesday Lisa's has 26 out of 30 and Mikey's has 14 out of
30. On Wednsday Lisa has 22 out of 30, Mikey 13 out of 30. On
Thursday Lisa has 18 out of 30, Mikey 12 out of 30. On Friday Lisa
has 14 out of 30, Mikey 11 out of 30. Saturday comes and they both
have 10 out of 30, which is equal to 1 out of 3.
First I drew a diagram of Lily's box speperated 1, 3/4/, 1/2/, 1/4, and zero. I drew mikey's
box seperate by eigth's. I went through for every four cups of Lily's cereal Mikey had one.
Eventually, both boxes ended at the zero mark.
On the Monday that Lily started with a new box, Mikey had 1/2 box
left. If m represents Mikey's consumption, then after they finished
their breakfast that day, Lily had 1-4m left in her box, and Mikey
had 1/2-m left in his box, considering the fact that Lily consumes 4
times as much cereal than Mikey. So if these are to be equal, I
needed to find what number m is. So I started with the equation 1/2m=1-4m.
1/2-m=1-4m
-m=1-4m-1/2
-m+4m=1-1/2
3m=1/2
m=1/6
I solved this equation and found out that m was 1/6, which was
Mikey's consumption rate, which made Lily's rate 2/3. So 1/2-1/6 was
1/3, and 1-2/3 was also 1/3, which was my answer.
1. First I began using random numbers to fit in the story. I began
with Lily having 30 pieces of cereal in her box.
This then means that Mikey has 15 pieces.
2. Then, since lily eats 4x as much as Mikey I took 4 from Lily for
each day and 1 from Mikey's for each day.
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Page 1 of 21
3. I continued this for 5 days I ended up with Lilly having 10
pieces of cereal and Mickey having ten pieces of cereal.
4. I then figured out that Micky ate 5 pieces of his 15 piece cereal
box which is 1/3. Also Lily ate 20 pieces of cereal from her 30
piece cereal box which is 2/3.
Student 5
Student 6
Student 7
1 whole=4/4. lily=1
whole, mikey= 1/2 of a
whole, If Lily eats 4
time as much and
Mikey then she will eat
3/4 of her box soon
mikey only eats 1/4
which = 3/4 gone
which makes both
boxes and equal
amount.
at the end of the week
they had 1/16 of cerial.
The problem describes
how a little girl and her
brother eat cereal. if
Lily eats four times as
much as mikey does.
on monday lily started
a new box and mikey
still had half a box left.
sometime during the
week they had the
same amount of cereal
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5. I decided to test this equation out for different numbers.
Ibtried it for lily having 100 pieces of cereal and Micky having 50
pieces of cereal. Two thirds of 100 is 66.66666667 which I rounded
to 66.7. One third of 50 is 16.66666667 which I rounded to 16.7. I
then found that 16.7 times four is 66.8 which is very close to 66.7.
Because these numbers were so close I exchanged them into my previous
problem. Micky has 50 pieces of cereal and eats 16.7 pieces a day.
Lily has 100 pieces of cereal and eats 66.7 pieces a day. After the
first day both had 33.3 pieces of cereal left.
Natalie and I, drew out the problem first. Then we used fractions to
plug in the numbers. To have an equal amount both boxes will have to
be 3/4 gone! which means lily ate 3/4 of her box while mickey only
ate 1/4............ 1/4+ 2/4= 3/4
1/2 divided by 4 equals 1/16 so they had 1/16
if mikey = x then Lily = 4x
Page 2 of 21
Student 8
Student 9
le
The problem of the
week asks what is the
fraction of a box that
each child had left in
the cereal box. If Lily
eats 4 times as much
as mikey does. On
Monday Lily started a
new box of cereal and
mikey had still a half
box left. Later that
week they
They both met at 1/6
left in there box of
ceral.
if x = mikey and 4x = Lily
im nort sure help
equation; 1-4x=1/2-x
sovel for x; 1/2=3x
x=1/6
prove it;
1-4/6=1/2-1/6
equal fractions;
6/6-4/6=2/6 or 1/3
3/6-1/6=2/6 or 1/3
Student 10
I think the two boxes
of cereal are 1/3 full.
they met at 1/6 of the box of ceral
The reason I got 1/3 full for both cereal boxes is because:
One box is only 1/2 full, while the other is full but eaten 4 times
faster. So I wrote an equation, with x as the amount of cereal eaten
and y is the amount of cereal left.
1-(4x) = y
1/2-(x) = y
Therefore:
1-(4x) = 1/2-(x)
I add 4x to both sides of the equation.
1 = 1/2+3x
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Page 3 of 21
I subtract 1/2 from both sides of the equation.
1/2 = 3x
Divide 3 from both sides of the equation.
(1/2)/3 = x
Simplify.
1/6 = x
Now I have the amount of cereal eaten by Mikey. We plug this into the
equations to get the answer.
1-(4x) = y
1-[4(1/6)] = y
1-(2/3) = y
y = 1/3 or 0.333...
I checked the answer by plugging it into the other equation.
1/2-(x) = y
1/2-1/6 = y
3/6-1/6 = y
y = 1/3 or 0.333...
Both equations had the same answer. The box is only 1/3 full.
Student 11
I conclude that there
should be 1/6th
remaining in each box.
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Reflection:
I think this problem was easy, because if you went to pre-algebra, you
would already know that if y = y, then the two equations used to get y
are equal too. The only tricky part was plugging it in. Some people
might take x to be the amount the box was full. They forgot about y as
they were solving for x, just like I did when I tried it on paper.
If Lily eats at a rate of four times greater than her brother than
the equation should look like and she started with a full box and he
started with a half box then the equations should look like the
following:
Page 4 of 21
Student 12
The amount of cereal
left in the boxes are
1/3 of the cereal box.
Student 13
They both have a
quarter left.
Student 14
They both had 1/3 of a
box left.
Student 15
There will be 1/3 of a
box of cereal left in
each box.
Student 16
Each child had 1/3 of a
cereal box left.
1-4x = 1/2 -x
O.K. First they told me that Lily had 1 new box of cereal and Mikey
had 1/2 of his cereal box. To to solve how much was left in each box
you have to make an equation. So my equation was 1-4x= 1/2-x. The 1
represents the box of cereal that Lily had and the 1/2 was the amount
of cereal left in Mikey's cereal box. Now Lily had four times as much
as Mikey. So let x equal how much Mikey eats per morning and let 4x
equal how much Lily eats per morning. Now solve for x. Subtract 1/2
from both sides and you get 1/2-4x=-x. Now add 4x to both sides and
you get 1/2=3x . Divide 3 from both sides and you get .5/3=x and you
finally get 1/6=x. Wait you still have to plug in x into your equation
to see how much is left over. You get 1-4(1/6)=1/2-(1/6). Solve and
you get 1/3=1/3 so you have 1/3 left in each box of cereal.
Since Lily started off with a new box and her brother had half. Then
later in the week they have the same amount.That means they have a
quarter of the cereal left.
1-4x=1/2-x
.5-4x=-x
.5=3x
2/6=x
1/3=x
First solve the equation: 1/2-X=1-4X. Solve for X. X=1/6. This means
that Mike ate 1/6 of 1/2 of a box of cereal leaving him with 2/6. It
also means that Lily ate 4(1/6) of a box of cereal leaving her with
2/6. Both children have 2/6 or 1/3 of a box of cereal left.
To solve this problem, I used algebra and an equation. First I
identified Mikey's rate of eating the cereal, which was x. Lily's was
4x, since she eats 4 times as much cereal as Mikey. Then, I set the
number of days it took for them to have the same amount of cereal as y.
As for the equation, I started off with Lily, which was 4xy, where the
4x represents how much she eats and the y as how many days it took.
After that, I completed the other side of the equation, Mikey's side,
which was 1/2 + xy, where the 1/2 represents the half of the cereal
box that was already eaten, and the xy representing how much he eats
(x), and the number of days it took (y).
Then, I simply simplified the equation, now 4xy = 1/2 + xy
First, I subtracted xy from each side, therefore canceling out the xy
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Page 5 of 21
on the right side of the equation. This left me with 3xy = 1/2. After
that, I divided both side by 3. To divide the 1/2 by 3, I simply
multiplied it by 1/3, and the result was 1/6. Therefore, Lily and
Mikey ended up with 1/3 of a box of cereal left on one day of the
week. Below is the steps I took for solving the equation, without words.
4xy = 1/2 + xy
-xy
-xy
_______________
3xy = 1/2
/3 /3
_______________
xy = 1/6*
*Remember, x represents how much Mikey ate, not how much is left.
To check my answer, I multiplied 1/6, the amount Mikey ate, with 4, to
see how much Lily ate. That equaled to 2/3. Then, I also added 1/2 and
1/6, to see how much was gone from Mikey's cereal box (the 1/2 was how
much was originally there before Mikey started eating it), which also
equaled to 2/3. Then I was sure, since 3/3 - 2/3 (the amount of cereal
gone from the box) = 1/3, that both children had 1/3 of cereal in the
box left.
Student 17
When Mikey and Lily
have the same amount
of cereal left, they will
each have 1/3 of the
box left.
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Reflection: This problem was a little harder than all of the other
problems. To set up the equation, I had to get help from my mom, so
bravo, mom! I was able to simplify and identify each part of the
equation easily, so the only part that I needed help was setting up
the equation. Again, I thank my mom who helped me solve this problem.
B = the amount of cereal in a full box.
x= the amount Mikey eats.
From the facts "Every morning at breakfast Lily eats four times as
much cereal Mikey does" and "On Monday Lily started with a new full
box, while Mikey still had half a box to finish" I turned the amounts
left in each of their cereal boxes into expressions. Lily eats B - 4x
every day,
while Mikey eats B/2 - x.
With those 2 expressions I then made the equation B - 4x = B/2 - x,
for the day their amounts of cereal left were the same.
Page 6 of 21
I then simplified the expression to B/2 = 3x, which simplified further
to x = B/6.
Therefore, Mikey has eaten B/6 while Lily has eaten 4B/6.
From their starting amounts, which was B/2 for Mikey and B for Lily, I
subtracted B/6 for Mikey and 4B/6 for Lily.
B/2 - B/6 = B/3
B - 4B/6 = B/3
Both of those calculations resulted in the same answer: B/3.
Reflections: This problem was the hardest of the POWs so far. The
biggest obstacle I encountered was how to create the right equation
accurately describing the situation. I had some help from my Dad on
that part.
Student 18
Each child had 1/3 of a
box left after the
second day.
First I made an algebraic expression using the information provided.
let x=amount consumed by Lily and t=number of days
Mikey: 1/2-(1/4x)t
Lily: 1-(x)t
Then from there I guessed and checked using pictures. The picture
for my final answer was two boxes split into 12 sections for Mikey
and Lily. I colored in 6/12 of the sections for Mikey becasue he
already ate 1/2of his cereal.
Then from day 1, I colored in 4/12 (1/3) of the sections for Lily.
One quarter of 4/12 is 1/12, so I colored in that much more for
Mikey. At the end of the day, Lily had 8/12 of a box left and Mikey
had 5/12 of a box left.
During day 2, Lily ate another 4/12 leaving 4/12 left in the box.
Mikey ate another 1/12 leaving 4/12 left in the box from the
previous day. At the end of Tuesday, Lily and Mikey both had the
same amount of cereal left in their boxes.
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Page 7 of 21
Student 19
Student 20
Later in the week, both
Lily and Mikey both
end up with 1/3 of a
box left
1.Sometime during the
week each child had
4/12 of the cereal box
left.
Reflections: I was stumped at first but then after disussing it with
my parents and a friend, I was finally able to figure out the
equation to the problem, leading to the answer.
I wrote an equation to help solve this question. Let x the amount of
cereal Mikey eats in one day.
1-4x=1/2-x
1/2 is equal to how much cereal is left in the box on Monday for Mikey
and 1 represents a whole box for Lily.
So the equation simplifies out to
1-4x=1/2-x
1=1/2+3x
1/2=3x
x=1/6
Then, we substitute 1/6 for x in the equation
1-4(1/6)=1/2-(1/6)
1-4/6=1/2-1/6
2/6=2/6
1/3=1/3
Therefore, later in the week,both Mikey and Lily would have 1/3 of the
box left.
REFLECTION
When I first worked on this problem, i got the first part of the
equation 1-4x=1/2-x but then couldn't go any further. After asking my
brother for help, I was easily able to solve it.
Each day Lily and Mikey each ate a fraction of the box. We don't
know what fraction each ate. I used trial and error using
different fractions. Each time I started with Mikey with a half a
box and Lily with a whole. Every time Mikey ate a fraction, lily ate
4 times as much. For example: On Mon. Mikey had 8/16 and Lily had
16/16. Then on Tues. Mikey had 7/16 (one less) and Lily had 12/16
(four less). On Wed. Mikey had 6/16 and Lily had 8/16. On Thurs.
Mikey had 5/16 and Lily had 4/16. this trial dosen't work because
Lily already has less.
Then i tried 10ths and it didn't work. After that I tried 12ths and
I found the answer.
M
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M
8/16
T
7/16
W
6/16
Th
5/16
F
S
S
Page 8 of 21
Student 21
Student 22
1/3 of the cereal box
The amount of cereal
left in both Mikey's
and Lilly's boxes is 1/3
of the box.
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L
16/16
12/16
8/16
M
L
5/10
10/10
4/10
6/10
3/10
2/10
4/16
M
6/12
5/12
4/12
L
12/12 8/12
4/12
Explanation: Lily first started out with a whole box and Mikey
started out with ½ of Lily’s. The variable n equals the amount of
cereal in a full box. Lily’s is n and Mikey’s is n/2. To find a
pattern I wrote the expression for Tuesday’s morning. Lily’s is
labeled as n-4m and Mikey’s is labeled as n/2-m. “m” is the amount
of Mikey’s cereal box in a day. Wednesday’s morning would also look
like Lily’s: n-8m and Mikey’s: n/2-2m. The variable x represents the
number of days passed or how many days you eat. If there were x days
that you have eaten the cereal, the equation would be n-4mx. Again,
n is the amount of Lily’s subtracting 4m, because Lily eats four
times Mikey, and times x, the x days that past. n-4mx would equal to
n/2-mx. n/2 equals the half the Mikey started with minus Mikey’s
cereal times the x, the x that represents the x days. Then the
equation would look like n-4mx=n/2-mx. I simplified the equation to
get n-n/2=4mx-mx. Again I simplified to n/2=3mx. To get n I divided
3 from each side and got n/6=mx. mx equals 1/6 so that means Mikey
ate that much and n/2-n/6 equals the amount that Mikey and Lily had
the same because n/2 was the half and subtracted with the amount
that he ate. So it got me 1/3 of the cereal of the box.
Reflection: I thought if I used guess and check, it was going to be
quick. However I needed help on composing equations so my dad
assisted how to make the algebraic equation. Step by step he
explained and I now know how to answer this question.
x = amount Lilly eats
1/2 - 1/4(x) = 1 - x
- 1/2
- 1/2
-1/4(x) = 1/2 - x
+x
+x
3/4(x) = 1/2
x = 2/3
Page 9 of 21
2/3 x 1/4 = 1/6 = how much Mikey eats
1/2 - 1/6 = 1/3
1 - 2/3 = 1/3
First, I set up an equation that had showed how much cereal was left
in Lilly's box on one side, and how much was left in Mikey's on the
other, and let x represent how much Lilly eats.
I know that Mikey eats 1/4 the amount Lilly eats so I put down '1/4
(x)'. But since he started out with half a box, I subtracted 1/4(x)
from 1-2.
I put 1 - x on the other side because I knew that Lilly started out
with 1 box and x represented how much she eats.
I solved for x and ended up getting x = 2/3.
I multiplied 2/3 by 1/4 to find out how much Mikey eats, which was
1/6.
To find out how much they had left in their box on the day it was
equal, I subtracted 1/2 by 1/6 to get 1/3. And I subtracted 1 by 2/3
to get 1/3.
Student 23
Each child had 1/3 of
the box left.
That shows that they had the equal amount of cereal left in their
boxes, which was 1/3 of a box.
Each child had 1/3 of the box left. To determine this,
I made an algebraic equation. I knew that Mikey began with 1/2
and Lily began with a full box or 1. I also knew that Lily ate 4 times
as much cereal as Mikey, so if Mikey ate x amount of cereal, Lily ate
4x. Since they were eating cereal, they were removing the previous total,
so the operation would be subtraction. Using these element, the equation
became:
1/2-x=1-4x
Then I solved:
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Page 10 of 21
-x + 4x = 1 - 1/2
3x = 1/2
x = (1/2)/3
x = 1/2*1/3
x = 1/6
so Mikey ate 1/6 more of his cereal. Now I substituted x to find how
much was left:
1/2 - 1/6
3/6 - 1/6
2/6 = 1/3
So 1/3 of the box was remaining. To check, I substituted x on the
other side:
1/3 = 1 - 4(1/6) ?
1/3 = 1 - 4/6
1/3 = 6/6 - 4/6
1/3 = 2/6
1/3 = 1/3 Yes
So we are sure that only 1/3 of the box of cereal is remaining.
Student 24
Lily and Mikey each
had one-eighth of a
box of cereal left.
Lily ate four times as much as Mikey so L=4M
Lily had one box and Mikey had a half a box so 4M=1/2
4M=1/2 I divided each side by 4
so M=1/8
Student 25
The fraction that each
child has in there
cereal box is 4/12.
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Each of them had 1/8 of a box left
When I saw this problem I immediatley did the guess and check
method. I first tryed 8ths but I realized that didn't work. I then
tried 12ths. I subtracted 1 12th from Mikey and 4 12ths from Lily.
At this point Mikey has 5 12ths and Lily has 8 12ths. I subracted
another 1 12th from Mikey, and 4 12ths from Lily. That made Mikey
have 4 12ths and Lily have 4 12ths. That means that each of them had
4 12ths later in the week.
Page 11 of 21
Student 26
Lily and Mikey had
one-third of their
cereal box left.
Lily and her little brother, Mikey, like different kinds of cereal
but their cereals come in the same size boxes. Lily eats four times
the cereal that Mikey does in the morning. Then on a random week
they noticed that on Monday Lily was starting a new box, while Mikey
was half way through his own cereal box. Then, later in that week,
they had the same amount of cereal. What fraction of a box did each
child have left?
The first thing we did was write an equation for the
relationship between the amount of cereal the two children eat.
L=the amount of cereal Lily ate and M=the amount of cereal Mikey
ate. Since Lily eats four times the amount of cereal Mikey does,
L=4M.
The second thing we did was write an equation for the amounts of
cereal the two children ate. 1-L=1/2-M. Replace L with 4M → 1 – 4M =
½ - M. Then bring the variable to the left, 1-4M + M= 1/2. Next, we
subtract 1 from both sides, using the addition property of equality,
to eliminate 1 on the left and bring ½ to -½, -4M + M = -½. Now we
collect like terms to make -4M + M = -½ to -3M = -½. Then we solve
to get M=1/6, that means Mikey ate 1/6 of his cereal box that
morning and since Lilly eats four times the amount of cereal Mikey
eats every morning, she ate 4/6 of her box, so Lily=4/6. Then 1 –
4/6 = ½ - 1/6, that means Lily and Mikey have 2/6 or 1/3 left in
their cereal box. So, Mikey and Lily = 1/3 of their cereal left.
Student 27
I came up with the
algebraic equation
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When Lily caught up to her brother they both had only 1/3 cereal
left in their box. Since she ate four times as much cereal each
morning, she was able to meet her brother before the end of the
week. We know this is correct because 2/6 and 1/3 are equal and they
are Lily’s and Mikey’s cereal amount left.
I started solving this by looking at the problem; it said that Lily
could eat 4 times as much cereal as Mickey could. I let 4x represent
Lily's eating speed and x represent Mickey's eating speed. I also saw
that it started on Monday and that they finished later in the week so
they only had 6 days to get the same amount of cereal. Also, I
noticed that Mickey started with half a box and Lily started with a
full box. To make the problem easier, I made the amount the box holds
a multiple of four, so I made the amount of cereal a box had 12. This
Page 12 of 21
meant that Mickey started with 6 cereals and Lily had 12 cereals. I
let x represent one to make it easier, so I let Lily eat 4 cereals a
day and Mickey eat one cereal a day. I know that is very little, but
it was to make the problem easier. I made a chart of Monday through
Saturday and I filled it out with the amounts they had left after
each day. Lily started with 12 went to 8 and then to 4 and then she
had to start a new box. Mickey started with 6 and then went to 5 and
to 4 and I noticed that they both had 4 on Wednesday. I saw that 4 is
a third of 12 which meant that they each had 1/3 the amount of cereal
in the box when they had the same amount.
Student 28
kkkkkkkkkkkkkkkkk
Student 29
I think Lily and MIkey
both have 1/3 of a box
left.
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Reflection: This problem was puzzling, but my brother was busy
working on his homework for Mrs. Embree's class and refused to help
me and my mom and dad were busy with their work and household duties
and I did not want to bother them so with much contemplation, I felt
that I got a decent answer. I looked in my email and saw an email I
got, but I didn't see the "answer" so I will add a question to my
reflection: Where is the "answer" in the email?
kkkkkkkkkkkkkkkkkkkkkkkkk
First, I used the strategy guess and check and make a table or
chart. I knew I had to figure out how many amounts were in the
cereal boxes. My first guess was, there was 40 amounts in the full
box of cereal. That wouls mean there was 20 amounts in 1/2 a box.
Well, I knew that LIly had 4 times as much as Mikey everyday. So, I
made a chart. Lily had started Monday with a full box, so I
wrote "full box" above her, and Mikey had started with a halt a box,
so I wrote "half box" above him. Now, for Lily, I took away 4
everyday, because she ate 4 times as much as Mikey.That would mean,
on Monday Lily had 36 amounts left, Tuesday-32, Wednesday-28,
Thursday-24, Friday-20, and Saturday-16. For Mikey I took away 1
everyday, because his sister had 4 times him, so he had 1/4 of her
amount, which was 1. So, Monday Mikey had 19 amounts left, Tuesday18, Wednesday-17, Thursday-16, Friday-15, and Saturday-14. Well,
that guess was wrong, because Lily and Mikey's amounts left were
never the same. My second guess was 30. That would mean that Mikey's
half a cereal box would be 15 amounts. I did things the same way I
did with the first guess, except the whole box as 30 amounts, and
the half box was 15 amounts, instead of 40 and 20. So, with 30
amounts in a whole box, I figured that Monday Lily would have had 26
Page 13 of 21
amounts left, Tuesday-22, Wednesday-18, Thursday-14, Friday-10, and
Saturday-6. For Mikey it would have been, Monday, he would have had
14 amounts left, Tuesday-13, Wednesday-12, Thursday-11, Friday- 10,
and Saturday-9. That was the correct guess! They both had 10 on
Saturday, and out of 30 that would be 10/30 or 1/3. So, 1/3 was my
answer!
I tried with algebra! couldn't find a way!
Student 30
On Friday, each child
would have 1/3 of a
box left.
~lani
I started out by making a chart. I was a little unsure at first
about the denominator of the fractions, but it all worked out:
Monday Tuesday Wednesday Thursday Friday Saturday
Lily- 24/24 20/24 16/24 12/24 8/24 4/24
mikey- 12/24 11/24 10/24 9/24 8/24 7/24
---I chose 24 for the denominator because that would be how may ounces
of cereal there were in a box. The only reason that I chose 24, not
23 or 25, was just because of the fact that it could be evenly
halved, and it was guess and check method. Because of the fact that
Lily ate 4 times as much cereal as mikey, I subtracted four from the
numerator each time instead of one, which I did with mikey. After I
got my results from the chart, I knew that I had to reduce the
fraction. 8/24 = 8 / 8 = 1/3
-- -24 / 8
If you wanted to use a formula for this problem, it would be very
easy to implement it into the problem:
12 - k = 24 - 4k
K would equal the amount of cereal that Mikey had eaten, with 4k
being the amount that Lily ate. 12 would be the number of ounces of
cereal that Mikey started with and 24 would be the number of ounces
that Lily started with. Since 4 was a factor of both 24 and 12, I
first thought to subtract 4 from 12 to see if that would be what k
equalled. Then multiplied 4 by 4 to get Lily's amount of cereal
eaten. When subtracting 4 from 12 and 16 from 24, the answer for both
was 8, so k = 4:
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12 - 4 = 8
4 x 4 = 16
24 - 16 = 8
Because of the fact that I figured out that k was four, I knew that I
had to add four days onto Monday, and that would end up with them
having 8 ounces of cereal left on Friday.
Student 31
Student 32
Student 33
My answer is I don't
know
Each child had 1/3 of a
box left when they
each had the same
amount of cereal in
their box.
The fraction of cereal
in both boxes is 1/3.
Reflection: At first, as I said before, I was unsure about my
denominator for my chart. I had first started out with 14, being 2
weeks, thinking that Mikey ate a box of cereal in 2 weeks, and Lily
did in one. Of coarse, I had forgotten the fact that Lily ate 4 times
faster than Mikey. This made me remember to read the problem
thoroughly, and pay attention to all the details. The chart kind of
gave me somewhere to go when I implemented the formula. I hope that
it helped all of you understand why I said what I did in the formula.
It was a good problem, though.
I don't Know
To start off I did one full box minus the number of days times four
times the amount that Mikey eats each day equals half of a box of
cereal minus the number of days times the amount that Mikey eats.
It looked like this. 1-n(4M)=1/2-n(M). Then I distributed the n on
both sides of the equation and got 1-4Mn=1/2-Mn. Then I subtracted
1/2 from both sides of the equation and got 1/2-4Mn=Mn. Then I
added 4Mn to both sides and got 1/2=3Mn. Then I divided by three on
both sides of teh equation and got Mn=1/6. The I went back and
substituted the 1/6 for everywhere that there was Mn. Then I got
1-4(1/6)=1/2-1/6. Then I simplified and got 1-4/6=1/3. Then did 14/6 and got 1/3=1/3. So when the children had the Lily and Mikey
had the same amount of cereal left in their boxes, they each had 1/3
left in their boxes.
AT first i identified the variable of the amount of cereal eaten by each person. I decided
that Mikey ate x amount of cereal each day and Lily ate 4x cereal each day. Then i had 1
equal Lilys box and 1/2 equal Mikeys Box. With this information i said 1-4x = 1/2-x.
The solution to the equation was 1/6. If i were to plug this number into Lilys expression it
would be 1-4(1/6)=1/3. If i pluged in 1/6 for Mikeys expression it would be
1/2-1/6=1/3. This proves that 1/3 of the cereal was left for Lily and Mikey.
WORK
x -amount of cereal Mikey eats
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Page 15 of 21
4x - amount of cereal Lily eats
1 - amount of cereal in box for Lily
1/2 - amount of cereal left for Mikey
1/2-x=1-4x
+4x +4x
1/2+3x=1
-1/2 -1/2
3x=1/2
3 3
x=1/6
Mikey/ 1/2-1/6=1/3
Lily/ 1-4(1/6)=1/3
Student 34
Each child had 1/3 of a
box left. This was a
test drive for MOM,
not the student
Student 35
Lily and Mikey had 2/6
or 1/3of a box left
when they had the
same amount of cereal
left in the box.
At some point in the week, both boxes have to contain equal amounts
of cereal. Lily started with 100%, Micky started with 50%. Lilly
eats 4 times as much as Micky. For whats left when both are equal
has to be represented as an equation. So Lily's side of the
equation is represented as 100%-4x, and Mikey side of the equation
is 50%-x, where x is what Mikey eats in one serving. These should
equal to one another:
100%-4x=50%-x, solving for x,
100%-50%=-x+4x
50%=3x
x=50%/3=16.67
Plugging in the x value into each side gives:
100%-4(16.67)=33.333%
50%-16.67-33.333%
Both Lily and Mikey are left with 33.333% or converting to fraction,
1/3 of the box.
I first substituted the amount Mikey ate that week with "x". Then
the amount Lily ate would be "4x". The equation that would tell the
amount of cereal left would be "1/2-x" for Mikey, because he started
eating cereal that was already half empty. The equation that will
tell the amount the cereal left for Lily would be "1-4x", since she
started eating with a full box, and she ate 4 times as fast as
Mikey. I wrote down the equation and started to simplify it.
1/2-x=1-4x
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1/2+3x=1
3x=1/2
x=1/6
That would mean that Lily ate 4/6, or 2/3 of a box that week,
because 1/6 times 4 is 4/6. Then, the amount of cereal that would be
left is 1-4/6. The answer is 2/6, or 1/3.
Student 36
Student 37
Mikey has 1/3th left
and Lily has 1/3 left
They each have a full
box of cereal.
Student 38
Using the equation 1n(L)=1/2-n(M) I figured
out that the amount of
the box left in the
children's boxes is 1/3.
Student 39
Lily and Mikey both
had 1/3 a box of cereal
left.
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Reflection:
I would like to thank my dad for giving me a simple advice; draw a
picture and substitute the amount Mikey ate with "x". Later on, I
figured out that amount Lily ate would be 4x, and I was able to
write the equation, and simplify it.
They start with one new box and half a box on Monday. So you
have to subtract 1/4 of Lily cereal.
We pretended each cereal box had 4 pieces.We started Mikeys
box with two and Lileys box have four.We pretended Mikey ate
one piece each day.Liley would of eaten a one box every day,
after two days they would have the same amount of cereal.
I used the equation 1-n(L)=1/2-n(M). The 1 at the beginning is 1 full
Box, The n is number of days they ate and the L is Lilly. Then I made
the equation 1-m(4M)=1/2-n(M) because L=4M. Then I distributed the n
to 4M and got 4MN. Then I distibuted the n on the other side and got
MN. So the equation then looked like 1-4MN=1/2-MN. I then combined
like terms or added MN to both sides and got 1-3MN=1/2. Then I
subtracted 1 from both sides and got -3MN=-1/2. I then divided both
sides by 3 to get MN=1/6. After I got MN=1/6 I plugged it into the
equation so 1-4(1/6)=1/2-1/6. Then I mutiplied 4 and 1/6 to get 2/3
and the equation was then 1-2/3=1/2-1/6. After that I subtracted and
got 1/3=1/3 so that means that the amount left in the box after days
of eating is 1/3.
To solve this problem, I used the equation "1-4x=1/2-x". I got
the "x" from the amount of cereal the Mikey eats per day and
the "4x" as the amount of cereal the Lily eats per day. The 1 in
front of the 4x is the amount of cereal in the box (a full box) and
the 1/2 in front of the x is for the half a box of cereal that Mikey
has. I solved this equation and got that "x=1/6". I plugged in 1/6
for x because it is the amount of cereal that Mikey eats per day and
got the equation of "1-4(1/6)=1/2-1/6". I solved that equation and
got 2/6 or 1/3 as the amount of cereal left in each of their boxes.
Page 17 of 21
Student 40
Student 41
Student 42
He had one fourths
and she had three
fourths.
They both had one
sixth of a box left.
They will meet when
they each have a box.
She eats faster than him so thats the answer if he eats slower, she eats faster.
First we set up 1-4x = .5 - x then we got rid of all the x, so it was
1 = .5+3x. then we divided both by 3, and got rid of the 3. so, it was
.5 over 3. So we multiplied .5 and 3 by 2, and the answer we came up
with was 1 over 6.
I set it up:
Lily Mikey
1 8/16
4/16 9/16
And so on ...
Student 43
sliandkl;a
Student 44
They both had 17/50
of their boxes.
Student 45
Both children have
8/14's by tuesday.
until I got that they met at one box. Lily had eaten two boxes when
Mikey finished his, according to my math.
jklfda; jfkadl; djkal;
I based the total amounts of cereal on 100 so that Lily had 100 left
and Mikey had 50 left. then I continually decreased the numbers by 4
and 12 until the numbers were even, my final number was 34 and i
started withh 100 so i simplified 34/100 to get 17/50.
L; starts new, Mon. 4, Tues. 4., Wed. 4, Thur. 4, Fri. 4, Sat. 4, Sun. 4
M; starts with half Mon. 7, 1, 1, 1, 1, 1, 1
Because on the week before both started w/ new boxes;
L; 4, 4, 4, 4, 4, 4, 4 =28
M; 1, 1, 1, 1, 1, 1, 1 =7
so 14 is a complete box.
Student 46
Mikey and Lily have
1/3 of their cereal box
left.
done by Dyanne Casillas p.3 math analysis
First, I wrote an equation to find the amount of cereal left using the
information given in the problem.
"1 - 4x" would be Lily's equation and Mikey's would be "0.5 - x"
The "1" in Lily's equation represents the full box of cereal she
started out with. The "0.5" represents the half of a box of cereal
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Page 18 of 21
Mikey started with. "4x" and "x" represents the amount of cereal they
eat every day.
1 - 4x = 0.5 - x
3x = 0.5
x = 1/6
I got this equation because they would have the same amount of cereal
left and the variable "x" would be the amount of cereal eaten.
"x = 1/6" which means that Lily eats 4/6 of the cereal box everyday
and Mikey eats 1/6 of his.
If they started on Monday, then this table will show what day they had
the same amount in their cereal boxes. They would have the same
amount of cereal left in their boxes on Tuesday, which means they had
2/6 which simplifies to 1/3 of their cereal left according to the data
table attached.
Student 47
Each child had 1/3 of
the box left.
First, I found a factor of 4 because that's how much more Lily eats
than Mikey, and I chose 12 as the total (full box).
Then for Mikey's cereal box I eliminated half of the box (6/12)
because he started out with half the box.
For day 1, Lily consumed 4/12 of the box leaving her with 8/12 of the
box left. While Mikey only consumed 1/12 of HALF the box leaving him
with 5/12 of the box left.
On day 2, Lily ate 4/12 more of the box from her remaining 8/12 so
that there was only 4/12 (1/3) of the box left. Mikey ate 1/12 of his
remaining 5/12 once more on day 2 so there was 1/3 of the box left.
Reflection: This problem was fairly confusing for me at first, because I
couldn't read the problem correctly and understand it. After a while, I
asked my brother for help and he assisted me in completing the
problem by making it more clear for me. Overall, this problem is much
easier once you understand it.
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Student 48
Student 49
My final solution was
that each child had 1/3
of their cereal box left.
Each child has 1/3 of a
box left.
Because the question stated that Lily ate 4 times as much as Mikey,
I came up with the equation: 4M=L. (M for how much cereal that Mikey
ate and L for how much cereal that Lily ate)
The amount of cereal they've have eaten during the week in addition
to the amount of cereal they have left later in the week is equal to
the amount they started with on monday.
I used this equation to figure out this problem:
1-x=4(1/2-x)
1-x is Lily's part of the problem. She eats the amount she has
started with on monday which is 1 cereal box subtracted by the
amount left at the very end which is x because we don't know what
the amount left is and we're trying to figure that out.
4(1/2-x)is Mikey's part of the problem. Lily eats four times what
Mikey eates; hence the 4 multipiled by the expresson in the
parentheses. Mikey eats the amount he has started with on monday
which is 1/2 a box subtractded from the amount left at the very end
which is unknown; hence 1/2-x.
To solve this I did distributive property first:
1-x=4(1/2-x)
1-x=2-4x
Then I moved all the x's to one side:
1-x=2-4x
1-2=-4x+1x
Then I soleved both parts of the problems and crossed out the
negative signs:
1-2=-4x=1x
1=3x
Therefore X=1/3 which means that each child had 1/3 of the box left
at the very end.
Reflection: This was very hard for me so I asked my sister to help
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Student 50
I think the answer is
1/3 of the cereal box.
me but she couldn't help me with the equation and so I went to my
dad for help. He explained how to solve the prblem by using an
equation and he also helped me with my explanation. I solved the
equation on my own, though. That part was easy.
I think this answer because if Lily its a 4 time the amount of ceral
of Mikey that has to be 1/3.
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