Problem 128 - 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 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

The maximum number of cement bags that can be lifted on the elevator in one trip is 39.

Step 1: Define the variables

Let's denote the number of cement bags by \(x\). The total weight of the cement bags is \(65x\), where 65 is the weight of one bag. The elevator operator weighs 265 pounds.

Step 2: Formulate the inequality

The total weight that the elevator can lift, which is the sum of the weight of the operator and the weight of the cement bags, is less than or equal to its maximum capacity. This situation can be described by the following inequality: \(265 + 65x \leq 2800\)

Step 3: Solve the Inequality

We isolate \(x\) by subtracting 265 from both sides of the inequality, then we divide by 65 to solve for \(x\). We'll have \(x \leq (2800 - 265)/65\)

Step 4: Compute the value

We plug the values into the equation to solve for \(x\). We get \(x \leq 39\). However, we are dealing with discrete units (the number of bags) which cannot be fractional. Therefore, the maximum number of cement bags that can be lifted is the largest integer less than or equal to 39. So, the number of bags that can be lifted is 39