Question

Terri and josh Goldman had a pottery stand at the annual craft fair. They sold some of their pottery at the original price of $10.50 each but later decreased the price of each by $3.00. If they sold all 85 pieces and took in $757.50, find how many they sold at the original price and how many they sold at the reduced price.

Answer 1

40 pieces are sold at original price,

45 pieces are sold at reduced price.

Explanation:

Let us assume the number of pieces sold at original price = x

Now, the total number of pieces sold = 85

⇒ Number of pieces pieces sold at ( original price + reduced price) = 85

or, The number of pieces sold at reduced price

= 85 - Number of pieces sold at original price = 85 - x

1 piece sold at original price costed = $10.50

⇒ The cost of selling x pieces at original price = x ( Cost of 1 original piece)

= x ($10.50) = 10.50x

Also, 1 piece sold at reduced price costed = $10.50 - $3 = $7.50

⇒ The cost of selling (85 - x) pieces at-reduced price

= (85-x) ( Cost of 1 reduced price piece)

= (85-x) ($7.50) = 7.50 (85-x)

Now, the all pieces are sold at $757.50

⇒ 10.50 x + 7.50 (85-x) = $757.50

or, 10.50 x + 637.5 - 7.5x = 757.5

or, 3 x = 757.5 - 637.5 = 120

or, x = 120/3 = 40

or, x = 40

hence, 40 pieces are sold at original price,

(85 -x) = (85 - 40) = 45 pieces are sold at reduced price.

Answer 2

40 pieces are sold at original price,

45 pieces are sold at reduced price.

Explanation:

Let us assume the number of pieces sold at original price = x

Now, the total number of pieces sold = 85

⇒ Number of pieces pieces sold at ( original price + reduced price) = 85

or, The number of pieces sold at reduced price

= 85 - Number of pieces sold at original price = 85 - x

1 piece sold at original price costed = $10.50

⇒ The cost of selling x pieces at original price = x ( Cost of 1 original piece)

= x ($10.50) = 10.50x

Also, 1 piece sold at reduced price costed = $10.50 - $3 = $7.50

⇒ The cost of selling (85 - x) pieces at-reduced price

= (85-x) ( Cost of 1 reduced price piece)

= (85-x) ($7.50) = 7.50 (85-x)

Now, the all pieces are sold at $757.50

⇒ 10.50 x + 7.50 (85-x) = $757.50

or, 10.50 x + 637.5 - 7.5x = 757.5

or, 3 x = 757.5 - 637.5 = 120

or, x = 120/3 = 40

or, x = 40

hence, 40 pieces are sold at original price,

(85 -x) = (85 - 40) = 45 pieces are sold at reduced price.