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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 10.50 ​each, but later decreased the price of each by ​$2.00. If they sold all 87 pieces and took in$ 791.50​, find how many they sold at the original price and how many they sold at the reduced price.

Answer 1

The reduced price is $10.50 - $2.00 = $8.50.

Assume they sold x items at $10.50. If they sold a total of 87 pieces, then 87 - x were sold at $8.50.

So the the equation is 10.50x + 8.50(87 - x) = $791.50

Use the distributive rule to eliminate the parentheses, combine like terms and solve for x.

Answer 2

So let's start with what we know - there were 87 pieces sold at either $10.50 or $8.50 for a total of $791.50. We can put this statement into two equations:

1. 10.50x + 8.50y = 791.50, where x is the number of bottles sold at $10.50 and y is the number of bottles sold at $8.50
2. x + y = 87

When you have two equations that are related to each other, you can use one to get the other down to a single variable. To do this, you first solve equation #2 for y.

x + y = 87

y = 87 - x

Next, you can plug this value of y into equation #1.

10.50x + 8.50(87 - x) = 791.50

Now you have an equation you can solve! Solve for x. Remember, x represents the number of pieces sold at $10.50.

10.50x + 8.50(87 - x) = 791.50

10.50x + 739.50 - 8.50x = 791.50

2x + 739.50 = 791.50

2x = 52

x = 26

Now that you know x, you can go back to equation #2 to solve for the real value of y.

x + y = 87

26 + y = 87

y = 61

Check your work quickly! Plug your new values for x and y into equation #1 to make sure you get the correct answer.

10.50x + 8.50y = 791.50

10.50(26) + 8.50(61) = 791.50

273 + 518.50 = 791.50

791.50 = 791.50

So there were 26 pieces sold for $10.50 (x in our formula) and 61 pieces sold for $8.50 (y in our formula)!