Word Problems Leading to Linear Inequalities

Problems involving inequalities are handled similarly to linear equations except for the sign that must definitely change.

Example 5.3.1:

Ade bought x biros at ₦8 each and (x + 4) rulers at ₦20 each. He spent less than ₦200. Form an inequality for the statement and solve it.

Solution: 

The biros cost ₦8x

The rulers cost ₦20(x + 4) or ₦(20x + 80)

⇒ Total cost will be ₦(8x + 20x + 80)

The total cost is less than ₦200

⇒ Then \( \scriptsize 8x \: + \: 20x \: + \: 80 < 200 \)

Hence \( \scriptsize 28x < 200 \: – \: 80 \)