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# Word Problems Involving Percent

When solving word problems that involve percent, it's good to keep in mind the three kinds of percent problems you could encounter based on variations of this statement:

"x percent of y is z"

1. If x is unknown, we might be asked "What percent of y is z?"
2. If y is unknown, we might be asked "z is x percent of what number?"
3. If z is unknown, we might be asked "What is x percent of y?"

## Percent word problem examples

The key to solving word problems involving percent is identifying which is the unknown variable.

Let's take a look at some examples.

## If x is the unknown variable

An auditorium has 200 seats and 165 are filled. What is the attendance at a percent of capacity? Or, what percent of 200 is 165?

We will start by writing a proportion.

$\frac{165}{200}=\frac{x}{100}$

We could cross multiply, but you might notice that the denominator on the left is twice the denominator on the right. So when we multiply both sides by 100, the new denominator on the left becomes 2 and x is by itself.

$x=\frac{165}{2}=82.5$

The answer is the auditorium is filled to 82.5% capacity.

## If y is the unknown variable

If a can of mackerel is 64% full and weighs 80 grams, what was the original number of grams of mackerel in the can? In other words, "80 is 64% of what number?" The unknown is y.

Write a proportion.

$\frac{80}{y}=\frac{64}{100}$

Cross multiply.

$64y=8000$

Divide both sides by 64.

$y=125$

There were originally 125 grams in the can.

## If z is the unknown variable

With 25 students in a classroom, 28% went to recess, 52% went to lunch, and the rest stayed in the classroom. What number of students stayed in the classroom?

The three percentages should total 100. Let's find the missing percentage:

$28+52+c=100$

$80+c=100$

$c=20$

Now, your question is "What is 20% of 25?" with the unknown being z.

Write a proportion.

$\frac{z}{25}=\frac{20}{100}$

Cross multiply.

$100z=500$

$z=5$

So, 5 students stayed in the classroom.

## Practice questions on word problems involving percent

a. If you've walked 55% of a total distance of 300 yards, how many yards did you walk?

$55%of300yards=0.55×300yards$

$=165yards$

b. Room A has 150 chairs. If 26% of the chairs are taken to Room B, 30% are taken to Room C, and the rest are left behind, how many chairs remained in Room A?

Chairs taken to Room $B=0.26×150=39\mathrm{chairs}$

Chairs taken to Room $C=0.30×150=45\mathrm{chairs}$

Total chairs taken $39+45=84\mathrm{chairs}$

Chairs remaining in Room $A=150-84=66\mathrm{chairs}$

c. If you ate 39 pieces of candy which was 15% of the total amount of candy – how much total candy was available at the start?

Let x be the total amount of candy. Then, $0.15×x=39$

$x=\frac{39}{0.15}$

$x=260$

d. If a 140-gallon tank is filled with 98 gallons of water, what percent of the tank is filled with water?

$\mathrm{Percentage filled}=\frac{98\mathrm{gallons}}{140\mathrm{gallons}}×100%$

$=0.7×100%$

$=70%$

## Get assistance learning about word problems involving percent

If your student is learning how to solve word problems involving percent, properly setting up a proportion or even identifying the variable to solve could be a bit tricky. Fortunately, a tutor can address your student's questions and concerns and even help them work on assignments or study for a test. The perks of tutoring can be tremendous. Learn more about how tutoring could benefit your student by contacting the Educational Directors at Varsity Tutors today.

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