In order to solve word problems involving percents, you should be able to:

Solving word problems involving percents is a

matter of taking the information from the problem and deciding where it belongs in the

percent formula.

The percent formula is as follows:

(the

**percent** written as a decimal value) x (the

**base**) = the

**amount**
**
**

The

**percent**, as indicated in the formula, is always expressed as a decimal value rather than in

percent form. The

**base** is sometimes considered the original value. It is the number that you are taking a percentage of. The

**amount** is sometimes thought of as the final answer. Let's lok at a few preliminary examples to make sure you understand how the

percent formula works before moving on to the word problems.

- What number is 12% of 80?

The percent, written as a decimal is 0.12. The

base is 80 and the amount is what we are looking for. So we have

(0.12)(80) = 9.6.

- 4.515 is 4.3% of what number?

The percent, written as a decimal is 0.043. The

base is not known and the amount is 4.515. So we have

- What percent of 400 is 3.2?

The

percent is what we are looking for. The

base is 400 and the amount is 3.2. So we have

Recall that in the

percent formula, percents are written as decimals. So the decimal form is 0.008 which means in

percent form we have 0.8%.

These three examples have shown you how to solve for each piece of the

percent formula. We now need to apply this information to solving word problems. Remember, the main task is to identify each piece of the

percent formula and then solve as we did above. Now let's use this process to work a word problem.

Suppose a retailer buys a coat for $80 and then sells it for $120. What is the

percent of markup on the coat?

The problem is telling us that we want to know the

percent value, so we need to identify the

**base** and the

**amount** to solve the problem. The value of $80 is our base. We have to be careful here because $120 is not the amount. When we take a percentage of $80, we then add that to the cost of the coat to get the selling price. In other words, the coat has been marked up $40. That is the amount we should be using. So we have the formula

Remember that when we solve the

percent formula for a percent, it gives us a decimal value that we have to change into a percent. In this case, the coat has been marked up 50%.