How many pieces sold?

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 ​$1.00 If they sold all 89 pieces and took in $1,133.50 find how many they sold at the original price and how many they sold at the reduced price?

Answer 1

Let x be the pieces sold at $13.50 and y be the pieces sold at $12.50

x+y=89

Subtract x from both sides

y=89-x

13.50x+12.50y=1133.50

Substitute

13.50x + 12.50(89-x)=1133.50

Distribute

13.50+1112.50-12.50x=1133.50

Combine like terms

1.00x+1112.50=1133.50

Subtract 1112.50 from both sides

x=21

y=89-21=68

So 21 pieces were sold at $13.50 and 68 pieces were sold at $12.50

Answer 2

A total of 89 pieces were sold.

A total of $1133.50 was received from the sale of all 89 pieces..

Some pieces (x) were sold for $13.50 each. For each piece sold at $13.50, they received $13.50(x).

Other pieces (y) were sold for $12.50 each. For each piece sold at $12.50, they received $12.50(y).

13.50x + 12.50y = 1133.50

x + y = 89

You can solve using substitution or elimination. I chose elimination in this instance.

The first equation remains unchanged.

13.50x + 12.50y = 1133.50

Each monomial or constant in the second equation is multiplied by 12.50.

12.50x + 12.50y = 12.50 (89) ====> 12.50x + 12.50y = 1112.50

Subtract the second equation from the first equation:

13.50x + 12.50y = 1133.50

-12.50x - 12.50y= -1112.50

1x=21 (when using elimination, one of the variables will be cancelled out or eliminated; here it was y)

x=21

It the total pieces sold = 89 and we just calculated that 21 were sold at 13.50, 68 must have been sold at 12.50:

x+y = 89

21+ y = 89

y= 68

check

13.50(21) + 12.50(68) = 1133.50

283.5 + 850 = 1133.50

1133.50 = 1133.50

check completed

21 were sold at the original price.

68 were sold at the reduced price.