Problem 22 - Prealgebra

Question

Solve each of these problems using the method developed in this section. You have decided to update your house by laying a new wood floor in your living room. Your floor has an area of 440 sq feu decide to buy enough flooring to allow for a certain amount of waste so you purchase 470 sq ft of wood flooring materials. Express your waste allowance as a percent. Round your result to the nearest percent.

Step-by-Step Solution

Answer

The waste allowance is 6%.

Step 1: Calculate the Waste in Square Feet

To determine the waste amount in square feet, subtract the area of the floor from the amount of flooring purchased. \[ \text{Waste} = 470 \text{ sq ft} - 440 \text{ sq ft} = 30 \text{ sq ft} \]

Step 2: Calculate the Waste as a Percentage

To find the waste as a percentage, divide the waste in square feet by the total purchased flooring, then multiply by 100. \[ \text{Waste Percentage} = \left( \frac{30 \text{ sq ft}}{470 \text{ sq ft}} \right) \times 100 \% \approx 6.38\% \]

Step 3: Round to the Nearest Percent

Round the calculated waste percentage to the nearest whole percent. \[ \text{Rounded Waste Percentage} \approx 6\% \]

Key Concepts

Waste Calculation

Waste calculation is an important concept in various fields, especially in construction and home renovation. When purchasing materials, it’s common to buy a bit more than the exact measurement required. This extra material is known as waste allowance. The need for waste arises due to:

• Irregularly shaped pieces that may be unusable.
• Mistakes during cutting or installation.
• Natural variations in material that might require discarding a portion.

To calculate waste, you subtract the actual needed amount from the total purchased amount. In our exercise, this was calculated by subtracting the living room area (440 sq ft) from the purchased wood flooring (470 sq ft), resulting in a waste of 30 sq ft. Knowing the waste amount helps in project management by ensuring you have enough material without significant shortages or surpluses.

Rounding Numbers

Rounding is a mathematical technique used to simplify numbers, making them easier to use and understand. In many real-world applications, exact values are not always necessary, and a rounded value can be more convenient. For percentages, we round to the nearest whole number because fractions of a percent are often negligible in practical terms. For instance, the waste percentage of 6.38% is rounded to 6% for simplicity. To round a number to the nearest whole number:

• Look at the digit in the tenths place (the first digit after the decimal point).
• If this digit is 5 or more, increase the number in the ones place by 1.
• If it is less than 5, keep the number in the ones place the same.

Rounding makes data easier to interpret and communicate, especially when precision is not critical.

Area Measurement

Area measurement is a fundamental concept in mathematics, used for determining the size of a two-dimensional space. It's particularly important in fields like architecture and home renovation. Area measurement is typically expressed in square units, such as square feet, square meters, etc. To calculate the area of a rectangular space, you multiply the length by the width. In the exercise, the area of the living room was 440 square feet. This value was crucial in determining the amount of flooring required and understanding the waste. Here’s how you can generally apply area measurement:

• Measure the dimensions of the space accurately – length and width.
• Use these measurements to find the area by multiplying them.
• Consider additional factors like alcoves or cutouts that might need extra material.

Understanding area helps in planning and ensures that estimates for materials are as accurate as possible.