Proportions can be very helpful in solving problems dealing with percents. Let’s look at this problem. Suppose a pair of shoes is on sale for 20% off of the original price.

If the original price is $85, how much money will you save? Keep in mind that a percent is a part out of a whole, and that whole is 100, when you’re dealing with a percent. So, 20% off, that would be 20 out of 100.

**Next Lesson:** Proportions in the Real World

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And now, we’ve set up our first ratio, and the key with proportions is to be consistent with your ratios. So, since our first ratio is the part out of the whole, then our second ratio also needs to be the part out of the whole. The whole, in this case, being your price. That’s the total cost, so that’s your whole. That’s your denominator, 85. And then the “how much money you save” is going to be your part, because you’re only going to save part of the whole. And since that’s what we’re trying to find, how much money will you save, that’s going to be our variable. So, we can just use an x or anything.

And then to solve our proportion, we’re going to cross multiply. So, we cross multiply 100 times x, which is 100x, is equal to 20 times 85. 2 times 85 is 170, and then we add a 0 for the 20, so 1700.

Then to solve for x, we have a 100 times x, and the opposite of multiplying is dividing. So, we divide both sides by 100. 100 divided by 100 is 1, times x is x. Cancel our two zeroes, 17 divided by 1 is 17. Therefore, if our $85 pair of shoes was 20% off, then we’d be saving $17 when we buy our shoes.

**Next Lesson:** Proportions in the Real World