Question

Kathi and Robert Hawn had a pottery stand at the annual skipcack craft fair. They sold some of their pottery at the original price of $9.50 for each piece, but later decreased the price by $2. If they sold all 90 pieces and took in $713, find how many pieces they sold at the original price and how many pieces they sold at the reduced price?

Answer 1

Answer: 19 pieces at original price and 71 pieces sold at reduced price.

Let x=number sold for original price, $9.50 and y = number sold at reduced price $7.50.
So we have 2 equations.
x+y=90 => x=90-y (eqn 1)
9.5x + 7.5y = 713. (eqn 2)
sub (eqn 1) => (eqn 2)
9.5(90-y) + 7.5y = 713
855-9.5y+7.5y = 713
855-713 = 2y
142 = 2y
y = 142/2
y = 71 (eqn 3)
sub (eqn 3) => (eqn 1)
x = 90 - 71
x = 19