word problem help

Question

A car dealer, at a year-end clearance, reduces the list price of last year's models by 15%. If a certain 4-door model has a discount price of $8000, what was its list price? How much can be saved by purchasing last year's model?

Answer 1

Madison,

 

Almost always, the unknown variable x represents in some way the question asked. So

 

Let x = the original list price of the car

     d = the decimal discount offered to sell the car (the inducement to snag a buyer)

 

The discount is stated in percent as 15%.  Divide that by 100 to get a decimal, so d = 0.15

 

The discounted selling price = (1 - d)x = (1 - 0.15)x = 0.85x = $ 8,000.00 which is given

So solve for x = 8000.00 / 0.85 = $ 9,411.76  which was the list price originally before the discount

And the saving = $ 9,411.76 - $ 8,000.00 = $ 1,411.76

 

Finally check it: 1,411.76 saving / 9,411.76 list price = 0.15  decimal or multiply by 100 to make it 15%.

Checks Out

Answer 2

The easiest way to solve this kind of problem is with a simple ratio:

 

8000/x =(100-15)/100

 

In this ratio, 8000 is the discounted price and x is the original price. This corresponds to the right side of the equation, where 100-15 (=85) represents the discounted price as a percentage and 100 is the denominator (representing the full, undiscounted cost of the car).  Solving  for x gives:

 

X=8000/(85/100)=9411.76

 

So the car originally cost $9411.76.

The amount saved is 9411.76-8000, or $1411.76