Chapter 8.8, Problem 60STP

To determine

Find the number of cases of juice Damon can buy.

Answer to Problem 60STP

Damon can buy at most 5 cases of juice.

Explanation of Solution

Given:

Damon can spend at most $150 on Supplies for a school party. He has already spent $78.80 on food and $29.95 on decorations. He plans to buy cases of juices that cost $8.25 per case. Write and solve an inequality to find the number of cases of juice Damon can buy.

Concept Used:

Let n represent the number of cases of Juice Damon can buy.

Damon can spend at most $150 on Supplies for a school party. He has already spent $78.80 on food and $29.95 on decorations.

At most $150 means $\le \text{ 150}$

Calculation:

Let n represent the number of cases of Juice Damon can buy.

Damon can spend at most $150 on Supplies for a school party. He has already spent $78.80 on food and $29.95 on decorations.

He plans to buy cases of juices that cost $8.25 per case.

Let n represent the number of cases of Juice Damon can buy.

  $\begin{array}{l}\text{78}\text{.80 + 29}\text{.95 + 8}\text{.25n }\le \text{ 150}\\ \text{108}\text{.75 + 8}\text{.25n }\le \text{ 150 }\\ \text{108}\text{.75 - 108}\text{.75 + 8}\text{.25n }\le \text{ 150 }\\ \text{8}\text{.25n }\le \text{ 41}\text{.25}\\ \frac{8.25\text{n}}{8.25}\le \frac{41.25}{8.25}\\ \text{n}\le 5\end{array}$

Damon can buy at most 5 cases of juice.

Thus, Damon can buy at most 5 cases of juice.