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Chapter 0: Problem 119

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?

Short Answer

Expert verified
The maximum number of cement bags that the elevator can safely carry in one trip is 28.

Step by step solution

01

Translate the problem into a linear inequality

Start by understanding what each number in the word problem represents. The maximum capacity of the elevator is 3000 pounds, the elevator operator weighs 245 pounds, and each bag of cement weighs 95 pounds. That means the weight of the operator plus the weight of the cement bags cannot exceed the maximum capacity of the elevator, forming the linear inequality: 245 + 95x 鈮� 3000, where x represents the number of bags.
02

Isolate the variable x

Solve the inequality for \(x\) by subtracting 245 from both sides: 95x 鈮� 2755.
03

Solve the inequality

Divide both sides of the inequality by 95: \(x \leq 28.95\). However, since we cannot have part of a bag, we must round it down to the nearest whole number.
04

Final Answer

The maximum number of cement bags the elevator can safely carry in one trip is 28 bags.

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