linear equations

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 ?$4.00. If they sold all 90 pieces and took in $ 685.0?0, find how many they sold at the original price and how many they sold at the reduced price.

Answer 1

Hi Alex,

 

First we need to define some variables

F = # items sold at full price ($10.50)

D = # items sold at discounted price ($10.50 - $4.00 = $6.50)

 

The 3rd sentence tells us

F + D = 90 and

10.5F + 6.5D = 685

 

Let's use elimination and multiply the first equation by -6.5

-6.5F - 6.5D = -585

10.5F + 6.5D = 685

 

Add these two equations together

 

4F = 100

F = 25

 

If there were a total of 90 pieces sold.

90 - 25 = 65 = D

 

25 items were sold at full price

65 items were sold at discounted price