Problem 62 - Prealgebra

Question

The space shuttle can carry a payload of about \(65,000\) pounds. If a compact car weighs about 2450 pounds, about how many compact cars can the space shuttle carry?

Step-by-Step Solution

Answer

The shuttle can carry 26 compact cars.

Step 1: Understand the Problem

To find out how many compact cars the space shuttle can carry, we need to divide the maximum payload the shuttle can carry by the weight of a single compact car. This means we will divide 65,000 pounds (the payload capacity) by 2,450 pounds (the weight of one car).

Step 2: Set Up the Division Problem

The division problem we need to solve is \( \frac{65000}{2450} \). This will determine how many times the weight of one car fits into the payload capacity of the shuttle.

Step 3: Perform the Division

Perform the division \( 65000 \div 2450 \). Calculating this gives approximately 26.53. This means the payload fits 26.53 times within the shuttle's capacity.

Step 4: Interpret the Result

Since we cannot carry a fraction of a car, we will round down to the nearest whole number. Therefore, the space shuttle can carry 26 compact cars.

Key Concepts

Division with Remainders

When you encounter a division problem, the goal is often to see how many times one number can fit into another. In our exercise, we asked ourselves how many compact cars, each weighing 2450 pounds, can fit into the space shuttle's payload of 65,000 pounds. This is a common real-life application of division.

However, often these division problems do not result in a whole number. They instead produce a remainder, which tells us what is left over after the division is complete. In our example, dividing 65,000 by 2,450 results in approximately 26.53. That .53 is part of the remainder, implying that a bit more weight is left after accounting for 26 full compact cars.

Understanding remainders is important:

• They help us see what is left after division.
• They show the practical limitations in real-world scenarios—like transporting physical items, where fractions are not feasible.

Payload Calculation

Payload calculation involves determining the total weight a vehicle can carry. In our context, the word 'payload' refers to the maximum carrying capacity of the space shuttle, which amounts to 65,000 pounds.

To determine this payload involves basic arithmetic operations:

• Identify the total capacity of the carrier (space shuttle).
• Identify the weight of the individual item to be carried (compact car).
• Use division to calculate how many of those items can be carried without exceeding that capacity.

Let’s recap our exercise: the space shuttle can carry multiple compact cars, each weighing 2,450 pounds. By dividing the shuttle's 65,000 pounds payload capacity by the weight of one car, we calculated the number of cars it can potentially carry. Understanding payload calculation helps in logistics and planning, ensuring safe and efficient transportation.

Rounding in Division

Rounding plays a critical role in division, especially when dealing with real-world applications. When we perform division and end up with a decimal, as with our calculation of 65,000 divided by 2,450 equating to approximately 26.53, we must consider how it affects the context.

There are several key points to keep in mind when rounding:

• In contexts where partial units (like half a car) don't make sense, such as transportation, round down to avoid exceeding limits.
• Rounding ensures that you adhere to practical and safe limits, particularly with weight and space constraints.

In our example, you can only transport whole cars, so rounding down to 26 cars is logical. This ensures that the shuttle does not surpass its payload limit, demonstrating how rounding can be both a mathematical necessity and a practical consideration.