Finding Percents in Word Problems

Percents are one of the types of math that we use the most in real life, which is probably why they lend themselves so nicely to word problems!

If you know how to find percents from all different angles (see our Percents Lessons), word problems are easy.  You can use a simple formula, or a proportion, fill in the items you know from the word problem, and solve.

Remember, "of" means multiplication in math.

For percent word problems, you want to use the proportion formula that works for all percent problems:

$\dfrac{part}{whole}=\dfrac{%}{100}$

In word problems, the part is usually the proportion that we care about (or that the word problem is asking about), the whole is the total number of objects in the word problem.

Example: A basketball player makes 3 out of every 5 free throws that she tries. What is her free throw percentages?

In this case, we need to figure out:

What are we talking about? Free throws.

What types of free throws do we care about? Free throws that she made.

What is the total that we are working with? The total number of free throws.

What is the percentage of free throws she made?  We don't know (this will be come our variable.)

Then, use the formula:

$$\eqalign{\dfrac{\text{part}}{\text{whole}}&=\dfrac{%}{100}\\\dfrac{\text{thing we care about}}{\text{total number of things}}&=\dfrac{%}{100}\\\dfrac{\text{free throws made}}{\text{total free throws}}&=\dfrac{%}{100}\\\dfrac{3}{5}&=\dfrac{x}{100}\\300&=5x&&\text{Cross multiply}\\\dfrac{300}{5}&=\dfrac{5x}{5}&&\text{Divide both sides by 5 to solve for x}\\x&=60&&\text{She makes 60% of her free throws}}$$

Just like in other percent problems, word problems give you different pieces of information.  You just have to know where to plug the information into the word problems.

Example 2: In a classroom of 35 students, 20% of the students are girls.  How many girls are there in the class?

In this case, we need to figure out:

What are we talking about? Students.

What types of students do we care about? Girls

What is the total that we are working with? The total number students in the class.

Note: in this case, we know the percent of girls, so you'll fill that in.  You don't know how many girls there are, so the number of girls will turn into a variable.

Then, use the formula:

$$\eqalign{\dfrac{\text{part}}{\text{whole}}&=\dfrac{%}{100}\\\dfrac{\text{thing we care about}}{\text{total number of things}}&=\dfrac{%}{100}\\\dfrac{\text{girls}}{\text{students}}&=\dfrac{%}{100}\\\dfrac{x}{35}&=\dfrac{20}{100}\\100x&=700&&\text{Cross multiply}\\\dfrac{100x}{100}&=\dfrac{700}{100}&&\text{Divide both sides by 100 to solve for x}\\x&=7&&\text{There are 7 girls}}$$

Example 3: A student scored 80% on a test.  She got 52 problems correct.  How many questions were on the test?

In this case, we need to figure out:

What are we talking about? Problems.

What types of students do we care about? Problems correct.

What is the total that we are working with? The total number problems on the test.

Note: in this case, we know the number of problems correct and the percent of problems correct, but we don't know the total, so that will be our variable.

Then, use the formula:

$$\eqalign{\dfrac{\text{part}}{\text{whole}}&=\dfrac{%}{100}\\\dfrac{\text{thing we care about}}{\text{total number of things}}&=\dfrac{%}{100}\\\dfrac{\text{problems correct}}{\text{total problems}}&=\dfrac{%}{100}\\\dfrac{52}{x}&=\dfrac{80}{100}\\5200&=80x&&\text{Cross multiply}\\\dfrac{5200}{80}&=\dfrac{80x}{80}&&\text{Divide both sides by 80 to solve for x}\\x&=65&&\text{There are 65 problems on the test.}}$$

Just like in regular percent problems, the formula above can be used for just about any percent word problem.  Write out the proportion, figure out what you know, fill in the numbers, and solve.