Question

The local sporting goods store is advertising a 20% off sale on a new ski coat. If the saleprice is $199, what was the original price of the ski coat?Use X in the equation

Answer 1

Let us call the original price x, shall we?

We are told that after the 20% off on x, the price is $199. Therefore, we can write this situation as

$x-\frac{20}{100}x=199$

Simplifying this gives

$\frac{80}{100}x=199\text{.}$

Alternatively, we could say that after 20% of on x, the sale price is now 80% of the original price. In which case, we have the equation

$\frac{80}{100}x=199.$

which is the same equation as we got first.

Now we need to solve for x. We do this by multiplying both sides by 100 and then dividing by 80:

$100\times\frac{80}{100}x=199\times100$$\Rightarrow80x=19900$

and dividing by 80:

$\frac{80x}{80}=\frac{19900}{80}$$\Rightarrow x=248.75$

Hence, the original price is $248.75.