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.

40 pieces are sold at original price,

45 pieces are sold at reduced price.

Step-by-step 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.

40 pieces are sold at original price,

45 pieces are sold at reduced price.

Step-by-step 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.