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Lesson 92: Problems Involving Discounts, Increases, and Decreases
This lesson discusses how to compute discounts, and percentage of increase and decrease. The lesson has many everyday applications.
Every day we see sale signs in stores that mention a certain "percent off." It's very easy to figure out how much money you'll actually be saving. For example, a $35.00 shirt is 10% off. How much money will you save? For this problem, we have a shortcut. If something is 10% off, just move the decimal point one space to the left. In this case, we get $3.50, which is the amount that you'll be saving. Of course you just have to subtract that amount to find out how much you will pay.
Many other percent discounts are easy to calculate without much math. For example, if something is 25% off, how much will we save? 25% is 1/4. To compute 1/4 of an amount, just divide it by 4. For example, what is 25% off a $40 sweater? 1/4 of $40 is $10, which is how much you save.
Another easy example is 50% off. That's just half. Divide the price by 2, and that is how much you save.
Let's say an item is discounted by some odd amount. For example, let's say it usually costs you $35 to fill up your gas tank, and now you hear that gas has gone down by 17% (we're pretending). How can you figure out how much you will save? First convert the percent to a decimal. Recall that we do that by moving the decimal two places to the left. We get 0.17. Now just multiply that decimal times the original amount. We multiply $35 times 0.17, and we get $5.95, which is how much we will save as a result of the price lowering.
Memorize this procedure: Amount x Discount (as a decimal) = Savings
Let's say that an item is increasing in cost. For example, you are told that your rent of $900 will go up by 3%. How can we figure out how much more we'll be paying? First convert the percent to a decimal, which is 0.03. Multiply the original amount times the decimal. We get $27, which is the amount of the increase. Of course, to figure out the new rent, just add the increase to the original amount.
Sometimes we want to figure out the percent that an item increased. This can help us determine if the increase was really significant. For example, if your rent is $2000/mo, and it increases by $5/mo, then percent-wise, it hardly matters.
As an example, say that a $45 item increases to $48. By what percent did it go up? First we have to figure out the actual amount of increase. We just subtract and see that it went up $3. Now we take the amount of increase, and divide it by the original price. We do $3 ÷ $45 and get 0.067 (rounding our answer). We must convert that to a percentage by moving the decimal point two spaces to the right, giving us 6.7%, the amount of increase.
We can use the same procedure to compute the percent that an item decreased. Just take the amount of decrease, and divide by the original price. Then proceed as above.
There will be more practice with these types of problems in later lessons. Memorize these procedures, but more importantly, make sure that you understand how and why they work. This way you'll always be able to do them.
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