A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the

BTGmoderatorDC wrote: ↑

Mon Feb 06, 2023 8:28 pm

A store purchased x sweaters for a total price of $750. If it sold all but four of them, each for $5 more than the average price it paid for a sweater, and in doing so earned a total profit of $30 on the original purchase, how many sweaters did it sell?

A. 21
B. 24
C. 26
D. 30
E. 35


OA C

Source: Veritas Prep

The average price paid for each sweater is 750/x.

The store sold (x - 4) sweaters for [(750/x) + 5 dollars] each and made a profit of 30 dollars; thus:

(x - 4)[(750/x) + 5] - 750 = 30

(x - 4)[(750/x) + (5x/x)] = 780

(x - 4)(750 + 5x)/x = 780

750x + 5x^2 - 3000 - 20x = 780x

5x^2 - 50x - 3000 = 0

x^2 - 10x - 600 = 0

(x - 30)(x + 20) = 0

x = 30 or x = -20

Since x can’t be negative, x = 30. So the store purchased 30 sweaters and sold 26 of them.

Answer: C