Word Problems Leading to linear Inequalities

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

Example 

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)

Total cost will be ₦(8x + 20x + 80)

The total cost is less than ₦200

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

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

\( \scriptsize 28x < 120 \)

\( \scriptsize x < \normalsize \frac{120}{28} \)

\( \scriptsize x < \normalsize \frac{30}{7} \)

\( \scriptsize x < 4 \frac{2}{7} \)