## 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 \$ 13.5

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.

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2 weeks 2022-01-12T18:34:49+00:00 1 Answer 0 views 0

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