Video Explanation

Text Explanation

Let's walk through this scene with some actual numbers first. If the price of a shirt at a store is $10, then without tax, you would just pay $10 for that shirt. However, when the tax gets included, the final amount you have to pay increases. So, if the tax happened to be 20%, the final amount you would have to pay is 10 + 0.20 × 10 = $12. This means that the dollar amount of tax can be calculated by subtracting the original retail price from the final amount, and we'll use this later on to determine the tax as a percent:

Since the problem tells us that the "original retail price" is R and since the "final amount" is the same thing as "the price including sales tax" (which the problem represents with the variable T), we would rewrite the above equation as:

Now, even though this problem is talking about "tax," it's really just another type of "percent increase" problem, and we can make use of the following formula to calculate the tax as a percent change:

Or, in the context of this problem involving tax:

Replacing those words with our variables gives us:

This makes answer choice (E) the correct answer.

We can also check our work by plugging in the values we used in the beginning example to see if we end up with a true equation:

True.