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Inequalities Word Problem

Fred bought 3 shirts, each of the same price and received less than $12 change from a $50 bill. What is the maximum cost of 1 shirt?

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Sep 23, 2015
Excellent Resource
by: Merri

This website is an excellent resource to help someone struggling with inequality word problems. The examples are not too complicated, but they take you through baby steps which is just what I needed.


Oct 09, 2013
Inequalities word problems
by: Bharathi


Your page is wornderful, the tips about the topic given are very useful Thanks a lot

Oct 07, 2013
Well done
by: Anonymous

This inequality word problem number has been very helpful to me. It has really made it clear for me regarding real world inequality problems. Gratis.
Florence Naggenda,
Kampala, Uganda.

Oct 01, 2012
really good web site
by: Anonymous

it helped a lot thank you

Nov 05, 2010
Inequalities Word Problem
by: Karin

What a great problem!

Let's first define our variable. What don't you know? We don't know the cost of the shirts. Since all of the shirts cost the same amount, we can let x represent the cost of the shirt.

Now, let's think about what happens in this situation when you go to the store. You hand the cashier a $50 bill and she (or the register) subtracts 3 times the cost of the shirt. Then you are given the change back, which was less than $12. But, You also know that you can't receive less than $0 in change.

Now let's write this situation using numbers.

Put your problem in the middle (50 - 3x), then on the left 0 is the least amount you will get back and on the right, you received less than 12. So, the amount you receive back is between 0 and 12.

0 < 50 - 3x < 12

Now we can solve the inequality.

0 <50 - 3x < 12

Step 1: Subtract 50 from all sides.
0-50 <50 - 50 - 3x < 12 - 50


-50 <-3x < -38

Step 2: Divide by -3 on all sides.
-50/-3 < -3x/-3 < -38/-3

Simplify and reverse your inequality symbol.

16.67 > x > 12.66666

x is greater than 12.66 and less than 16.67.

Therefore, the maximum amount that the shirt can cost is $16.66.

Now check:

50 - 3(16.66) =0.02

Hope this helps,

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