Problem 8 - Thinking Mathematically

Question

In Exercises 5-8, one more piece of information is given than is necessary for solving the problem. Identify this unnecessary piece of information. Then solve the problem. An architect is designing a house. The scale on the plan is 1 inch - 6 feet. If the house is to have a length of 90 feet and a width of 30 feet, how long will the line representing the house's length be on the blueprint?

Step-by-Step Solution

Answer

The unnecessary information is the house's width. The length of the house on the blueprint would be 15 inches.

Step 1: Identify unnecessary information

In this problem, the unnecessary data is the width of the house. We don't need this information to find out the length of the line on the blueprint.

Step 2: Understand the scaling

According to the scale on the blueprint, \(1\) inch represents \(6\) feet.

Step 3: Compute the length

Now, to find the length in inches of the blueprint line that represents \(90\) feet, we'll perform the following calculation: \((90 \, feet) \, / \, (6 \, feet/inch) = 15 \, inches\)

Key Concepts

Identifying Unnecessary Information

When tackling a mathematical word problem, one crucial skill is identifying unnecessary information. Unnecessary information is any part of the problem's text that does not contribute to finding the solution. In the given exercise, we are asked to find the line's length on the blueprint for a specific dimension of a house. While we have both the house's length and width, our task only involves calculating the line representing the house's length. Therefore, the width is considered unnecessary. By focusing on what's essential, we simplify problem-solving and avoid being distracted by irrelevant details. Remember, not all information given is always needed. Carefully determine what the problem asks, and filter out details that aren't required.

Understanding Scale Models

Scale models are representations or drawings of something real, but smaller or larger while maintaining the proportions. In architecture, blueprints typically use a specific scale to represent real-life dimensions in manageable sizes. Here, the scale given is 1 inch to 6 feet. This means each inch on the blueprint corresponds to 6 real feet of the house dimensions. Understanding this concept allows us to perform conversions from the actual size to the model (or vice versa). It ensures accuracy in drafting and real construction. The scale acts as a bridge between the model and reality, allowing us to foresee and plan accurately in the design process.

Mathematical Calculations

Mathematical calculations help us find precise measurements or results. In problems like this, calculations are straightforward when the scale is well understood. We had a scale of 1 inch to 6 feet. When calculating how long the line for a 90-foot length will be, we use a simple conversion calculation. First, we take the actual length, which is 90 feet, and divide it by 6 feet per inch, the given scale. This gives us:

• 90 feet ÷ 6 feet/inch = 15 inches.

This means that on the blueprint, the line representing the 90-foot length of the house will be 15 inches long. Understanding the relevant math allows us to seamlessly convert real-world dimensions into accurate blueprint measurements, which is essential in fields requiring precision.