The CD Amnesiac by Radiohead has a list price of 1798 and th

The CD Amnesiac, by Radiohead, has a list price of $17.98, and the CD Hail to the Thief, by Radiohead, has a list price of $18.98. If a store\'s total sales of both CDs is 253 CDs and the total revenue of both CDs is $4762.94, how many of each CD were sold?

Solution

let the number of CD Amnesiacs sold be x

price of each CD Amnesiac = $17.98

==> price of x CD Amnesiacs = 17.98x

let the number of CD Hail to the thief sold be y

price of each CD Hail to the thief = $18.98

==> price of y CDs Hail to the thief = 18.98y

Total number of sales = 253

==> x + y = 253 ----------- (1)

Total revenue = $4762.94

==> 17.98x + 18.98y = 4762.94 -------- (2)

Solving (1) and (2)

17.98* (1) - (2) ==> 17.98 x + 17.98 y - (17.98x + 18.98y) = 17.98(253) - 4762.94

==> 17.98 x + 17.98 y - 17.98x - 18.98y = 4548.94 - 4762.94

==> -0.98y = -214

==> y = -214/0.98

==> y = 218.367 = 218

substitute y = 218 in (1)

==> x + 218 = 253

==> x = 253 - 218

==> x = 35

Hence number of CD Amnesiacs sold = 35

number of CD Hail to the thief sold = 218