Question

5. Suppose you are the manager of a music store. At the end of one week you are going over

receipts for the previous week's sales. Three hundred and seventy five compact discs were
sold. One type of compact disc sold for $12.95 and another sold for $14.95. The total
compact disc receipts were $5306.25. The cash register that was supposed to record the
number of each type of compact disc sold malfunctioned. How many of each type of
compact disc were sold?

Answer 1

Explanation:

x = cheaper compact disc

y = more expensive compact disc

x + y = 375.....x = 375 - y

12.95x + 14.95y = 5306.25

12.95(375 - y) + 14.95y = 5306.25

4856.25 - 12.95y + 14.95y = 5306.25

4856.25 + 2y = 5306.25

2y = 5306.25 - 4856.25

2y = 450

y = 450/2

y = 225 <==== there were 225 of the more expensive compact discs sold

x + y = 375

x + 225 = 375

x = 375 - 225

x = 150 <==== there were 150 of the cheaper compact discs sold

check...

12.95x + 14.95y = 5306.25

12.95(150) + 14.95(225) = 5306.25

1942.50 + 3363.75 = 5306.25

5306.25 = 5306.25 (correct)