Help me solve this problem

Question

A department store buyer purchased some shirts for $540. Then she sold all but eight of them. On each shirt sold, a profit of $6 (over the purchase price) was made. The shirts sold brought in revenue of $780. To help you answer the questions, use the following to help derive an equation. Let x represent the number of shirts bought initially. How many shirts were initially purchased and at what price?

(a) Express the number of shirts sold in terms of x.

(b) Express the purchase price for each shirt in terms of x.

(c) Express the selling price for each shirt in terms of x.

(d) Utilize the fact the number of shirts sold (a) times the selling price (c) brought in a revenue of $780 to derive an equation that you can solve and answer the questions.

Answer 1

Help me solve this problem

A department store buyer purchased some shirts for $540. Then she sold all but eight of them. On each shirt sold, a profit of $6 (over the purchase price) was made. The shirts sold brought in revenue of $780. To help you answer the questions, use the following to help derive an equation. Let x represent the number of shirts bought initially. How many shirts were initially purchased and at what price?

(a) Express the number of shirts sold in terms of x.

(b) Express the purchase price for each shirt in terms of x.

(c) Express the selling price for each shirt in terms of x.

(d) Utilize the fact the number of shirts sold (a) times the selling price (c) brought in a revenue of $780 to derive an equation that you can solve and answer the questions.

S = number of shirts

x = price

S*x = 540

6(S - 8) = 780

S = 540/x

6(540/x - 8) = 780

3240/x - 48 = 780

3240/x = 828

3240/828 = x

x = 3.913 cost per shirt

S(3.91) = 540

S = 138 shirts bought

138 - 8 = 130 shirts sold.

130 shirts sold.