Question

Kathi and Robert Hawn had a pottery stand at the annual Skippack Craft Fair. They sold some of their pottery at the original price of​ $9.50 for each​ piece, but later decreased the price of each piece by​ $2. If they sold all 90 pieces and took in ​$729​, find how many pieces they sold at the original price and how many pieces they sold at the reduced price.

Answer 1

Answer:27 pieces were sold at the original price.

63 pieces were sold at the new price

Explanation:

Let x represent the number of pieces of pottery that was sold at the original price.

Let y represent the number of pieces of pottery that was sold at the new price.

They sold some of their pottery at the original price of​ $9.50 for each​ piece. This means that the amount that they got from selling x pieces of pottery at the original price would be 9.5x

They later decreased the price of each piece by​ $2. This means that the new price was 9.5 - 2 = $7.5

This means that the amount that they got from selling x pieces of pottery at the new price would be 7.5y

If they sold all 90 pieces and took in ​$729​, then the equations are

x + y = 90

9.5x + 7.5y = 729 - - - - - - - - - -1

Substituting x = 90 - y into equation 1, it becomes

9.5(90 - y) + 7.5y = 729

855 - 9.5y + 7.5y = 729

- 9.5y + 7.5y = 729 - 855

- 2y = - 126

y = - 126/- 2 = 63

Substituting y = 63 into x = 90 - y, it becomes

x = 90 - 63 = 27