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There are a few problems relating to percents that anybody might come across in everyday life and want to solve. I am going to show you how to solve a few of these problems, no matter how they are presented, whether it be to find the percent of a number or to find the answer to a percentage word problem. You will also learn how to easily find a percent increase.

## Problem 1: Find x% of y

In retail, clerks often need to know the price after a discount. I’m going to present two solutions to this problem. The first uses a calculator and the second is just a simple trick one can use to solve the problem quickly in their head.

### With a calculator:

To find any percentage of a number, simply multiply the number by the percent in decimal form.

**Example:** A $67 coat is on sale for 20% off. How much is the coat after the discount?

**Solution:** multiply the price, $67, by the percent in decimal form. 20% is .20 in decimal form. So the discount is 67 * .20 = 13.40 and to find the price of the coat, we’ll take the original price minus the discount, so $67 – $13.40 = $53.60.

**Example: **A bill is $34. How much would a 15% tip be?

**Solution:** Multiply the total of the bill by the percent in decimal form, so .15, to get 34 * .15 = 5.1. So the amount to tip is $5.10.

### In your head:

Now, to solve these problems in your head you will just need to know how to move a decimal point. Finding 10% of a number is easy. All you have to do is move the decimal point one place to the left. So 10% of $34.00 is $3.40. If you want to know what 20% of the number is you’ll just take 10% 2 times, since 10% + 10% = 20%. So 3.40 + 3.40 = 6.80. If you want to know what 25% is, just take 10% 2 and a half times, so 3.40 + 3.40 + 1.70 = 8.5.

This makes it easy to find a tip or a discount. To find the discounted price, just take the discount minus the full price.

## Problem 2: What percent of y is z? or (x%) * y = z

You can fit many percent problems into this formula. In math, the word “of” translates to times (multiplication) and the word “is” translates to equals. So the word problem can be written as: (x%) * y = z. You will always know at least two of the variables (the letters in the equation). Plug them in and solve!

**Example:** If you received a box of 50 books and 4 of them were damaged, what percentage of the shipment was damaged?

To solve this, first we will need to fit it into the formula. What percent of the shipment of 50 books is damaged? Plug it into our formula and we have (x%) * 50 = 4. To solve for z, we just need to divide both sides by 50 to obtain .08. Convert the decimal to percent by moving the decimal two places to the right: 8%.

8% of the books in the box were damaged.

## Problem 3: Percent increase (Present – past) ÷ past

If sales on Christmas eve this year was $3600 and the sales last year was $2900, what is the percent increase?

(3600 – 2900) ÷ 2900 = .24

Convert the decimal to percent by moving the decimal two places to the right: 24%

The increase in holiday sales was 24%.

## 4 comments

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