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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.

Respuesta :

Answer:

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.

Answer:

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.

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