MORE PRACTICE USING ALGEBRA TO SOLVE PROBLEMS...
1) The first stage of a rocket burns 28 seconds longer than the second stage. If the total burning time for
both stages is 152 seconds, how long does each stage burn?
2) In a student election, 584 students voted for one or the other of two candidates for president. If the
winner received 122 more votes than the loser, how many votes were cast for each candidate?
3) The sum of Alan's age and Bob's age is 40. The sum of Bob's age and Carl's age is 34. the sum of
Alan's age and Carl's age is 42. How old is each person?
4) The sum of the ages of David, Tom and Jim is 34. David is three years older than Jim and Tom is 5
years younger than Jim. How old is each person?
5) Gilda is looking at the skateboards in the window of Thunder Mountain Sport store. The Blue Thunder
skateboard costs $8.47 more than the Silver Streak skateboard, but $12.95 less than the Wizard
skateboard. The three skateboards together costs $160.00. How much does each skateboard cost?
6) Lydia was selling tickets for the school play. She sold 10 more adult tickets than children tickets and
she sold twice as many senior tickets as children tickets. A total of 210 tickets were sold for the play.
How many of each type of ticket were sold?
7) Robert wanted to buy a long distance calling card to place a call overseas. One card advertised a rate
of $1.25 for the first minute and then $0.75 for each additional minute. Another card advertised a rate
of $0.85 per minute. If he wants to talk for 25 minutes, which card would give him the better rate?
8) Jeremy wants to make some extra money delivering newspapers on the weekends. He gets paid
$0.50 for each paper that he delivers, as well as a set amount of $5.50 for organizing all of the flyers in
the newspapers. If he wanted to make enough money to purchase a new iPod for $95, how many
papers does he need to deliver?
Solutions on the next page…
1)
Let FS represent the first stage, and SS represent the second stage.
FS = SS + 28
2)
FS + SS = 152
[SS + 28] + SS = 152
2SS + 28 = 152
2SS = 152 – 28
SS = 124 /2
SS = 62 seconds
So, FS = 90 seconds
Let w represent the number of votes for the winner, and y represent the remaining votes.
w = y + 122
3)
and
and
w + y = 584
[y + 122] + y = 584
2y + 122 = 584
2y = 584 – 122
y = 462 /2
y = 231 votes
So, w = 353 votes
Let A represent Alan's age, B represent Bob's age, and C represent Carl's age.
A + B = 40
and
B + C = 34
and
A + C = 42
So, using the first two equations, we know that A = 40 – B and C = 34 – B.
If we substitute these into our 3rd equation, we get…
[40 – B] + [34 – B] = 42
74 – 2B = 42
We need to bring -2B to the right side so that it is positive, and 42 to the left side.
74 – 42 = 2B
So, 2B = 32
And B = 32 /2, or 16.
If Bob is 16, then Alan must be 24, and Carl must be 18.
4)
Let D represent David's age, T represent Tom's age, and J represent Jim's age.
D=J+3
and
T=J–5
and
D + T + J = 34
Using the first two equations, we can use substitution in solving the 3rd equation.
D + T + J = 34
[J + 3] + [J - 5] + J = 34
3J – 2 = 34
3J = 34 + 2
J = 36 /3
J = 12
So, David is 15 years old, Tom is 7 years old, and Jim is 12 years old.
5)
Let B, S, and W represent each of the three skateboards.
B = S + 8.47
B = W – 12.95
and
and
B + S + W = 160
So… S = B – 8.47, and W = B + 12.95.
We can use these for substitution in the 3rd equation…
B + [B – 8.47] + [B + 12.95] = 160
3B + 4.48 = 160
3B = 160 – 4.48
B = 155.52 /3
B = 51.84
So, B is $51.84, S is $43.37 and W is $64.79.
6)
Let a represent adult tickets, c represent children tickets, and s represent senior tickets.
a = c + 10
and
s = 2c
and
a + c + s = 210
We can use the first two equations for substitution in the 3rd equation…
a + c + s = 210
[c + 10] + c + [2c] = 210
4c + 10 = 210
4c = 210 – 10
c = 200 /4
c = 50
So, 50 child tickets, 60 adult tickets, and 100 senior tickets were sold.
7)
Let m represent the number of minutes.
1st card…
1.25 + 0.75 (m – 1) = 1.25 + 0.75 (24)
↓
↓
1st minute
Remaining
minutes
= 1.25 + 18
= $19.25
2nd card…
0.85m = 0.85 (25)
= $21.25
Therefore, the 1st card will give him the better rate.
8)
Let n represent the number of newspapers.
0.50n + 5.50 = 95
0.50n = 95 – 5.50
n = 89.50 /0.50
n = 179
Therefore, 179 newspapers need to be delivered before Jeremy can afford his new iPod.