Question

A car is normally priced at $12000. In anticipation of their Labor Day Sale, the dealership raises the price of the car by 15%, and then puts the car on sale from that price at 15% off. What is the sale price of the car?

Answer 1

$11,730

Explanation:

I'm going to work this two ways - first step by step, then all together.

Step by step:

We have a car with a value of $12,000. The dealership first raises the price by 15%:

`12,000xx0.15=1800` - so the price increase is $1800 and the car is now on sale for:

`$12,000 + $1800 = $13,800`

And then the dealership announces a 15% off sale. What's the price of the car now?

`13,800xx0.15=2070` - this is the price reduction, and so the final price of the car is:

`13,800-2070=11,730`

And so the "sale" isn't much of one at all - buyers only save

`$12000-$11730=$270`

And now, all at once (I'll build the equation step by step):

We have the Old Price of the car (I'll call that `OP`) and the New Price of the car (I'll call that `NP`):

`OP=NP`

and we know that the Old Price is 12,000:

`12000=NP`

Now what do we do to the Old Price? First we increase it by 15%:

`12000(1+0.15)=NP`

and then we reduce the whole thing by 15%:

`(12000(1+0.15))(1-0.15)=NP`

and now we can solve:

`(12000(1.15))(0.85)=NP`

`(13800)(0.85)=NP`

`11730=NP`