Chapter 8.7, Problem 10GP

To determine

Write and solve an inequality to find how many tables she must clean to earn at least $120.

Answer to Problem 10GP

At least 28 tables she must clean

Explanation of Solution

Given:

Isabel earns $50 plus $2.50 for each table she cleans. Write and solve an inequality to find how many tables she must clean to earn at least $120.

Concept Used:

Translate the sentence into an inequality.

Isabel earns $50 plus $2.50 for each table she cleans. Find how many tables she must clean to earn at least $120.

At least means the inequality sign $\ge$

Let the number of table she cleans represent by x

The required inequality: $50+2.50x\ge 120$

Calculation:

Let the number of table she cleans represent by x

The required inequality: $50+2.50x\ge 120$

  $\begin{array}{l}50+2.50x\ge 120\\ 50-50+2.50x\ge 120-50\\ 2.50x\ge 70\\ \frac{2.50x}{2.50}\ge \frac{70}{2.50}\\ x\ge 28\end{array}$

Thus, at least 28 tables she must clean.