# Determining Percent Increase and Decrease

Formation involving percentages is fairly easy to decipher. If you’re 45 percent finished with a project, for instance, you know that you’re almost half done. Percents are based on the idea of how many out of 100, so the comparison of the percentage to the total amount is quick and universally understood.

You’re probably confronted with percent increases and decreases on a daily basis. For example, you may deal with salary increases or decreases. Citing these changes as percentages is easier when it comes to comparing the changes. One person’s increase of \$2,000 per year, for instance, is much different from another person’s increase of the same amount — especially when one person currently earns \$10,000 and the other earns \$100,000.

## Working with Percent Increase

A percent increase isn’t just an increase in the original amount; it’s a comparison to the original amount. When you get a 5% increase in salary, you get what you originally earned plus an additional 5% of that original amount. If you’re told the dollar amount of your increase and want to determine what percent that increase is, you compare the amount of the increase to the original amount.

### Computing new totals with increases

You can add or subtract percent to get their sums or differences; the answers in these cases are in percentages. But when mixing percentages with numerical amounts, such as money or time, you have to change the percent to a decimal before multiplying.

When figuring the amount resulting from a particular percent increase, you change the percent to a decimal and then multiply by the original amount. After you have the amount of the increase, you add that amount to the original number to get the new total. Or, if you want one-stop computing, you can add the percentage value of the increase to 100%. Then you change the total percentage to a decimal, multiply by the original amount, and have the new total amount as a final result.

### Solving for the original amount

With the basic equation used to solve for the percent increase (refer to the previous section), you can solve for either the percent increase, the increased amount, or the original amount — as long as you’ve given the other two values. I could give you three different formulas or equations, one to solve for each of the values, but it’s easier to just remember one formula and perform some simple algebra to solve for what’s missing.

Imagine you’re told that all the prices in a store increased by 41 ⁄2% last year. You have a list of all the current prices and want to determine the original price of an item. To do so, you just have to use the formula for a percent increase (provided in the previous section). You fill in the percentage and the new price, let the original price be represented by x, and then solve for x. Check out the following example for practice.

### Looking into Percent Decrease

Computing percent decrease has a lot of similarities to computing percent increase — you change percent to decimals, you multiply by the original amount, and then you refer to the original amount. However, sometimes the math is just a bit trickier because you subtract rather than add (subtraction is a more difficult operation for most folks). And the amount of the decrease often gets obscured (you end up computing with a number that wasn’t in the original problem) when you find the reduced amount directly, without subtracting. I explain everything you need to know about computing percent decreases in the following sections.

### Figuring out the percent decrease

Say you purchase several thousand dollars worth of office supplies and are given a volume discount on the entire order. Your bill just shows the total before the discount and the net cost after the discount. You can determine the percentage of the discount by using the formula for percent decrease.

### Last word

If you purchase a piece of machinery after getting the frequent customer discount of 10%, you may want to determine the original cost for insurance purposes. To find out that original cost, you use the formula for determining the percent decrease. You let the original amount be represented by x, and then you solve for x in the equation after replacing the other quantities with their respective values.