The usual selling price

Question

the usual selling price of a car was $104,000. It was later sold at a 10% discount and a 17% profit was made. Find the loss that would have been made if it had been sold at a 30% discount.

Answer 1

Regardless of whether we are considering a car or something else, the initial (base) amount used to compute percent is the most misunderstood part of percent problems.

Percent Increase = (new amount – original amount)/(original amount)

 

Percent Decrease = (original amount – new amount)/(original amount)

 

To sell a car for a 10% discount when the usual selling price is $104,000 means:

     Percent Decrease = (original amount - new amount)/(original amount)

                10% = (104000 - x)/104000

                10/100 = (104000 - x)/104000

                  10*1040 = 104000 - x

                     x = 104000 - 10400

                     x = 93600       The car was sold with a 10% discount for $93,600.

 

Percent Profit = (Selling price – Wholesale Price)/(Wholesale Price)

               17% = (93600 – w)/w

               (17/100)w = 93600 – w

                 117w = 9360000

                       w = 80000     

             The car was purchased wholesale for $80,000 and sold for a 17% profit at $93,600.

 

Had the car been sold at a 30% discount (from the usual price of $104,000):

       0.30 = (104000 – z)/104000

        z = 104000 – 0.3(104000)

        z = 72800     To sell the car at $72,800 means a profit of:

                       (selling price – purchase price) = ($72,800 -$80,000) =  -$7,200.

                         This is a LOSS of $7,200.

Answer 2

at a 10 percent discount, means the car was sold for 104,000 - 104,000(.1) = .9(104,000) = 93600

 

If 17 percent profit were made, this means the car initially cost 83 percent of this price at which it was sold, so

93,600 * .83 = 77688 --> price of car

 

If the car were sold at a 30 percent discount, this would mean it was sold at 104,000*(1-.3) = 104000(.7) = 72800

 

Since the price of the car was 77688 and it was sold for 72800, there is a loss of 77688 - 72800 = $4,888