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 $ 13.50 ​each, but later decreased the price of each by ​$3.00. If they sold all 91 pieces and took in $ 1 comma 030.50​, find how many they sold at the original price and how many they sold at the reduced price.

Answer 1

Answer: they sold 25 at the original price they sold 66 at the reduced price.

Step-by-step explanation:

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

Let y represent the number of pottery that they sold at the reduced price.

They sold a total of 91 pieces of pottery. This means that

x + y = 91

They sold some of their pottery at the original price of $ 13.50 ​each, but later decreased the price of each by ​$3.00. The reduced price would be 13.5 - 3 = $10.5

If they made $1030.5 in total, it means that

13.5x + 10.5y = 1030.5 - - - - - - - - - 1

Substituting x = 91 - y into equation 1, it becomes

13.5(91 - y)+ 10.5y = 1030.5

1228.5 - 13.5y + 10.5y = 1030.5

- 13.5y + 10.5y = 1030.5 - 1228.5

- 3y = - 198

y = - 198/ - 3

y = 66

x = 91 - y = 91 - 66

x = 25