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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