Percentage word problems

Before you learn about percentage word problems, review formula for percentage or you can use the approach that I use here.

Example #1:

A test has 20 questions. If peter gets 80% correct, how many questions did peter missed?

The number of correct answers is 80% of 20 or 80 / 100 × 20

80 / 100 × 20 = 0.80 × 20 = 16

Recall that 16 is called the percentage. It is the answer you get when you take the percent of a number.

Since the test has 20 questions and he got 16 correct answers, the number of questions he missed is 20 − 16 = 4

Peter missed 4 questions.

Example #2:

In a school, 25% of the teachers teach basic math. If there are 50 basic math teachers, how many teachers are there in the school?

I shall help you reason the problem out!

When we say that 25% of the teachers teach basic math, we mean 25% of all teachers in the school equals number of teachers teaching basic math.

Since we don't know how many teachers there are in the school, we replace this with x or a blank.

However, we know that the number of teachers teaching basic math or the percentage = 50

Putting it all together, we get the following equation:

25% of ____ = 50 or 25% × ___ = 50 or 0.25 × ____ = 50

Thus, the question is 0.25 times what gives me 50?

A simple division of 50 by 0.25 will get you the answer

50 / 0.25 = 200

Therefore, we have 200 teachers in the school

In fact, 0.25 × 200 = 50

More percentage word problems


Example #3:

24 students in a class took an algebra test. If 18 students passed the test, what percent do not pass?

Set up the problem like this!

First, find out how many student did not pass.

Number of students who did not pass is 24 − 18 = 6

Then, write down the following equation:

x% of 24 = 6 or x% × 24 = 6

To get x%, just divide 6 by 24

6 / 24 = 0.25 = 25 / 100 = 25%

Therefore, 25% of students did not pass.

If you really understand the percentage word problems above, you can solve any other similar percentage word problems.

Example #4:

A department has a total of 22,000 units of stock. 25% of the garments are black and 10% of the garments are size 14.

a) How many black garments are there?

b) How many size 14 garments are there?

c) If 10% of the black garments are size 14,how many garments are black and size 14?

Solution

25% = 25 per 100 = 250 per 1000
For 22,000 just multiply 250 by 22

250    ×    22   =  250 × (10 + 10 + 2)

                       =  2500 + 2500 + 500
                       =  5000 + 500
                       =  5500

So, there are 5500 black garments.

10% = 10 per 100 = 100 per 1000
For 22,000 just multiply 100 by 22
100 × 22 = 2200

If 10% or 10 per 100 of the black garments are size 14, then 100 per 1000 of the black garments are size 14.

500 per 5000 are size 14.

What is 10% of 500?

10% = 10 per 100, so 50 per 500.
So 550 of the black garments are size 14.

If you still do not understand them, I strongly encourage you to study them again and again until you get it. The end result will be very rewarding!

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