Download GSM-243 - Math 416

GSM-243
Chapter Review 6 ANSWER KEY
1. The perimeter of a rectangle is 48 meters. The measure of the length is 12 meters
greater than the measure of the width. What are the dimensions of the rectangle?
x = length
1) 2x + 2y = 48
y = width
2) x = y + 12
Ans: Length = 18 m
Width = 6 m
2. The length of a rectangle is nine meters less than three times the width. If the
perimeter of the rectangle is equal to 78 meters, find the dimensions of the
rectangle.
x = length
1) x = 3y – 9
y = width
2) 2x + 2y = 78
Ans: Length = 27 m
Width = 12 m
3. The length of a picture is 0.4 meters less than twice its width. To frame it, 7.6
meters of framing are needed. Find the dimensions of the picture.
x = length
1) x = 2y – 0.4
y = width
2) 2x + 2y = 7.6
Ans: Length = 2.4 m
Width = 1.4 m
4. The width of a rectangle is eight meters less than the length. The perimeter is 76
meters. Find the dimensions.
x = length
1) y = x – 8
y = width
2) 2x + 2y = 76
Ans: Length = 23 m
Width = 15 m
5. A movie theatre charges $5.25 for two small popcorns and a drink. The same
theatre charges $8.90 for three small popcorns and two drinks. Find the price of
each.
x = price of a small popcorn
1) 2x + y = 5.25
y = price of a drink
2) 3x + 2y = 8.90
Ans: Price of a small popcorn = $1.60
Price of a drink = $2.05
6. One integer is four more than the other. The sum of the two integers is 246. Find
the integers.
x = 1st number
1) x = y + 4
y = 2nd number
2) x + y = 246
Ans: 1st number = 125
2nd number = 121
7. The sum of two integers is 112. One of the integers is 72 less than the other
integer. What are the integers?
x = 1st number
1) x = y – 72
nd
y = 2 number
2) x + y = 112
Ans: 1st number = 20
2nd number = 92
8. The difference between two natural numbers is eight. One of the numbers is twice
the other number. Find the natural numbers.
x = 1st number
1) x – y = 8
nd
y = 2 number
2) x = 2y
Ans: 1st number = 16
2nd number = 8
9. The difference of two integers is 18. One integer is one-third of the other integer.
What are the integers?
x = 1st number
1) x – y = 18
y = 2nd number
2) y = 1/3x
Ans: 1st number = 27
2nd number = 9
10. A post-office clerk sells some 8-cent and 11-cent stamps for a total of $2.80. The
number of 8-cent stamps is three times the number of 11-cent stamps. How many
of each stamp were sold?
x = # of 8¢ stamps
1) 0.08x + 0.11y = 2.80
y = # of 11¢ stamps
2) x = 3y
Ans: # of 8¢ stamps = 24
# of 11¢ stamps = 8
11. A man has $3.70 in coins, consisting of 9 less quarters than dimes. How many of
each coin does he have?
x = # of dimes
1) y = x – 9
y = # of quarters
2) 0.10x + 0.25y = 3.70
Ans: # of dimes = 17
# of quarters = 8
12. A collection of nickels and quarters has a value of $7.15. There are twice as many
quarters as one third the number of nickels. How many quarters and nickels are
there?
x = # of quarters
1) 0.25x + 0.05y = 7.15
y = # of nickels
2) x =2(1/3)y
Ans: # of quarters = 22
# of nickels = 33
13. The sum of our present ages is 41. If I live 17 more years, after doubling my
present age, I will be 9 years less than your present age. What are our present
ages?
x = My present age
1) x + y = 41
y = Your present age
2) 2x + 17 = y – 9
Ans: My present age = 5
Your present age = 36