Problem 128 - College Algebra Essentials

Question

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 2800 pounds. If the elevator operator weighs 265 pounds and each cement bag weighs 65 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Step-by-Step Solution

Answer

At most, 38 bags can be safely lifted on the elevator in one trip.

Step 1: Identify Relevant Information

There is a maximum weight of 2800 pounds for the elevator. The operator weighs 265 pounds. Each cement bag weighs 65 pounds. Let's define \(x\) as the number of cement bags.

Step 2: Formulate the Inequality

Remembering the weight limit of the elevator, the sum of the weight of the operator and the cement bags cannot exceed 2800 pounds. Therefore, we can write the inequality as \(265 + 65x \leq 2800\)

Step 3: Solve the Inequality

Subtract 265 from both sides of the inequality to isolate the term with \(x\): \(65x \leq 2535\). Next, divide both sides of the inequality by 65 to solve for \(x\): \(x \leq 39\)

Step 4: Interpret the Solution

The solution \(x \leq 39\) means that 39 or fewer bags of cement can be safely raised on the elevator in one trip. However, since we cannot have a fraction of a bag, we must round down to the nearest whole number if a fraction is obtained. Therefore, a maximum of 38 bags can be safely lifted at a time.