Problem 129 - College Algebra

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 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Step-by-Step Solution

Answer

The safest number of cement bags that can be lifted on the elevator in one trip is 29.

Step 1: Understanding the problem

Let's denote the number of cement bags as \( x \). The maximum weight the elevator can carry is 3000 pounds. The operator weighs 245 pounds and each cement bag weighs 95 pounds. The total weight on the elevator would therefore be \( 245 + 95x \) pounds.

Step 2: Formulating the inequality

The sum of the weights of the elevator operator and the cement bags should not exceed the elevator's maximum capacity. Thus, the following inequality holds: \( 245 + 95x \leq 3000 \).

Step 3: Solving the inequality

To solve for \( x \), we first isolate \( x \) on one side by subtracting 245 from both sides, resulting in \( 95x \leq 2755 \), and then dividing both sides of the inequality by 95, giving us \( x \leq 29 \). So, the number of cement bags, \( x \), can be at most 29.