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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Nov 05, 2010
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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

Simplify:

-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,
Karin

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