Question

70 POINTS!! You buy a video game system for $259 that, is 31% off the original price. What is the original price of the system this system explain?
students answer- 259 times 0.31 = 80.29 259 plus 80. 29 = $339.29

What mistake did the student make? Explain how to answer the question correctly.

Answer 1

Answer:

The students mistake was that he took 31% of the new price and added it to the new price. He should have taken 69% of his new price and added it to his new price. The original price was $375.36

Step-by-step explanation:

Lets work it out and compare our work. Since its 31% off, the formula we need to use is original times percent off equals the new price. Let x equal the original.

x*.69=259

Divide both sides by .69

(x*.69)/.69=259/.69

Divide

x=375.36

The original price was $375.36

The students mistake was that he took 31% of the new price and added it to the new price. He should have taken 69% of his new price and added it to his new price.

Answer 2

Answer:

375.36 = original price

The student needs to determine what percentage of the original price the sale price is and divide by that instead of multiplying.  You cannot add to determine the discount since you do not know the original price.

Step-by-step explanation:

The sale price of the video game is equal to the original price  minus the discount.  The discount is equal to the original price  times the percent off.

Sale price = original price - discount

                  = original price - original price* discount percent

Factor out the original price

Sale price =original price (1-discount percent)

The sale price is 259  and the discount percent is 31

259 = original price (1-.31)

259 = original price (.69)

Divide by .69 on each side

259/.69 = original price *.69/.69

375.36 = original price

The student needs to determine what percentage of the original price the sale price is and divide by that instead of multiplying.  You cannot add to determine the discount since you do not know the original price.