SOLUTION: 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 $11.50 each, but later decreased the price of

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Question 1054860: 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 $11.50 each, but later decreased the price of each by $3.00. If they sold all 99 pieces and took in $ 931.50, find how many they sold at the original price and how many they sold at the reduced price.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
11.50 - 3.00 = 8.50.

some of the pieces of pottery were sold at 11.50 and some of the pieces of pottery were sold at 8.50.

let x = number of pieces of pottery sold at 11.50.
let y = number of pieces of pottery sold at 8.50.

since a total of 99 pieces of pottery were sold, and since the total revenue collected was 931.50, you get the following equations.

x + y = 99
11.50 * x + 8.50 * y = 931.50

the first equation says that the total number of pieces of pottery sold was 99.

the second equation says that the total money collected was 931.50, when x were sold at 11.50 and y were sold at 8.50.

these two equations need to be solved simultaneously.

we'll solve by elimination.

multiply both sides of the first equation by 11.50 and leave the second equation as is to get:

11.5 * x + 11.5 * y = 1138.5
11.5 * x + 8.50 * y = 931.5

subtract the second equation from the first to get:

3.00 * y = 207

divide both sides of that equation by 3 to get y = 69.

since x + y = 99, this means that x has to be equal to 30.

your solution is that x = 30 and y = 69.

this means that the number of pieces of pottery sold at 11.50 is 30 and the number of pieces of pottery sold at 8.50 is 69.

30 * 11.50 + 69 * 8.50 is equal to 931.50.

solution looks good.

they sold 30 at the original price and 69 at the reduced price.