1. Solve the following word problem.
The perimeter of a rectangle is The width is 2 times its length. Find the dimensions of the rectangle.
Let: L = length W = width
2L + 2W = 24
Solve the system
W = 2L
2L + 2(2L) = 24
W = 2L
2L + 4L = 24
W = 2(4)
6L = 24
W = 8
L = 4
Length is 4 and Width is 8

2. 11.04 Using Systems to solve Word Problems (Coin / Money)

3. To solve a word problem using a system:
1) read the problem carefully
2) assign variables and set up a system
3) solve the system
4) answer the question
A word problem that involves money will have decimals in the equations when you set up the system.
Remove the decimals by multiplying
all the terms by 100.

4. Solve the following word problem.
A man has 18 coins in his pocket, all dimes and quarters.
When counted, he has $ How many of each coin are there?
Let: d = dimes q = quarters
d + q = 18
Solve the system
.10d q = 3.60
Clear the decimals from the 2nd equation, multiply by 100.
d + q = 18
d + q = 18
10d q = 360
d = 18
10d q = 180
d = 6
– 10d – 25q = – 360
__________________
– 15q = – 180
q = 12
6 Dimes and 12 Quarters

5. Solve the following word problem.
The difference of the value of dimes and nickels is $0.60.
The sum of the value of dimes and nickels is $1.40.
How many of each coin are there?
Let: n = nickels d = dimes
.10d – .05n = .60
Solve the system
.10d n = 1.40
Clear the decimals from both equations, multiply by 100.
10d – 5n = 60
10d + 5n = 140
10d + 5n = 140
__________________
10(10) + 5n = 140
20d = 200
n = 140
5n = 40
d = 10
n = 8
10 Dimes and 8 Nickels

6. Solve the following word problem.
Six apples and 3 bananas cost $4.95.
Six apples and 5 bananas cost $5.45.
Find the cost of each apple and each banana.
Let: a = apples b = bananas
6a + 3b = 4.95
Solve the system
6a + 5b = 5.45
Clear the decimals from both equations, multiply by 100.
600a b = 495
6a + 3b = 4.95
600a b = 545
6a + 3(.25) = 4.95
600a b = 495
6a = 4.95
– 600a – 500b = – 545
6a = 4.20
____________________
a = 0.70
– 200b = – 50
b = 0.25
Apples $ Bananas $0.25

7. Solve the following word problem.
3 adult tickets and 4 child tickets cost $24.25.
5 adult tickets and 3 child tickets cost $31.25.
Find the cost of each adult and child ticket.
Let: a = adult c = child
3a + 4c =
Solve the system
5a + 3c =
Clear the decimals from both equations, multiply by 100.
300a c = 2425
3a + 4c =
500a c = 3125
3a + 4(2.50) =
1500a c =
3a =
– 1500a – 900c = – 9375
3a =
______________________
a = 4.75
1100c = 2750
c = 2.50
Adult $ Child $2.50