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?

1 Answer

Answer:

$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#