Problem 111 - Introductory Algebra for College Students

Question

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 elevator can safely lift 29 bags of cement in one trip.

Step 1: Determine the Weight Available for Cement Bags

Subtract the weight of the elevator operator from the maximum capacity of the elevator. This can be done by using the formula: Available weight = Maximum capacity - Operator's weight. Here, the maximum capacity is 3000 pounds and operator's weight is 245 pounds. So, available weight = 3000 - 245 = 2755 pounds.

Step 2: Calculate the Number of Cement Bags

Divide the weight available for cement bags by the weight of each cement bag in order to determine the number of cement bags. This can be done using the formula: Number of bags = Available weight / Weight of each bag. Here, the available weight is 2755 pounds and the weight of each bag is 95 pounds. So, number of bags = 2755 / 95.

Step 3: Round Down the Number of Bags

Since you cannot have partial bags, round down the result to the nearest whole number. This is done so as not to exceed the maximum capacity of the elevator.

Key Concepts

Problem Solving

When confronted with a problem, the first step is understanding the scenario you are dealing with. In this case, you are tasked with figuring out how many cement bags an elevator can carry. Each aspect of the problem - the elevator's maximum capacity, the weight of the operator, and the weight of the cement bags - plays a crucial role in finding the solution.

• First, identify all given data, such as the maximum capacity and specific weights.
• Next, find out what is being asked - here, it's the maximum number of bags.
• Finally, use logical steps to work toward finding the solution while ensuring all parts of the problem are considered.

Approaching problems systematically helps in breaking down complex issues into manageable parts. This step-by-step strategy is essential not only in algebra but in various real-life scenarios as well.

Weight Calculation

Weight calculation involves determining how much weight can be supported based on specific constraints. In our elevator problem, we need to calculate the available weight capacity by removing the weight of the elevator operator from the total capacity. We do this using subtraction.

• Start with the total capacity, which is 3000 pounds.
• Subtract the operator's 245-pound weight.
• This gives us the total weight available for cement bags, which is 2755 pounds.

Understanding how to calculate weight helps ensure that we work within safe limits and aligns with practical applications such as safe load handling and conveyance limitations.

Division and Rounding

After calculating the available weight—2755 pounds—our next step is to find out how many complete bags of cement can be loaded. We do this using division by the weight of an individual cement bag, which is 95 pounds.

• Perform the division: 2755 divided by 95, resulting in approximately 28.947 bags.
• Because we cannot load a fraction of a bag safely, we use rounding.
• Round down to the nearest whole number, which results in 28 bags.

Rounding down ensures that the weight does not exceed the safe limit. This practice is common in scenarios where partial quantities cannot be used or must be whole, especially when safety and precision are critical factors.