2. A rectangular room measures 13 feet by 15 feet. It is going to be carpeted with carpeting that sells for $68 per square yard. a. What is the area of the room in square feet? b. If the scale of the room drawing is 4 inch = 1 foot, give the dimensions of the room in inches on the scale drawing. c. A yard equals 3 feet. How many square feet are in a square yard? d. How many square yards will it take to carpet the room? Round up to the next greater integer
2. A rectangular room measures 13 feet by 15 feet. It is going to be carpeted with carpeting that sells for $68 per square yard. a. What is the area of the room in square feet? b. If the scale of the room drawing is 4 inch = 1 foot, give the dimensions of the room in inches on the scale drawing. c. A yard equals 3 feet. How many square feet are in a square yard? d. How many square yards will it take to carpet the room? Round up to the next greater integer
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Problem Statement
**Given:**
A rectangular room measures 13 feet by 15 feet. It is going to be carpeted with carpeting that sells for $68 per square yard.
**Questions:**
a. What is the area of the room in square feet?
b. If the scale of the room drawing is 1/4 inch = 1 foot, give the dimensions of the room in inches on the scale drawing.
c. A yard equals 3 feet. How many square feet are in a square yard?
d. How many square yards will it take to carpet the room? Round up to the next greater integer.
### Solutions:
**a. Calculating the Area of the Room in Square Feet:**
To find the area in square feet:
\[ \text{Area} = \text{Length} \times \text{Width} \]
\[ \text{Area} = 13 \, \text{ft} \times 15 \, \text{ft} \]
\[ \text{Area} = 195 \, \text{square feet} \]
**b. Converting Room Dimensions to Scale Drawing Dimensions:**
Given the scale: 1/4 inch = 1 foot, we convert the room dimensions to inches.
\[ \text{Length in inches} = 13 \, \text{ft} \times \frac{1}{4} \, \text{inch/ft} = 3.25 \, \text{inches} \]
\[ \text{Width in inches} = 15 \, \text{ft} \times \frac{1}{4} \, \text{inch/ft} = 3.75 \, \text{inches} \]
So, the dimensions of the room on the scale drawing are 3.25 inches by 3.75 inches.
**c. Calculating Square Feet in a Square Yard:**
A yard equals 3 feet, so:
\[ \text{1 Square Yard} = \left(3 \, \text{ft} \times 3 \, \text{ft}\right) \]
\[ \text{1 Square Yard} = 9 \, \text{square feet} \]
**d. Calculating Square Yards Needed to Carpet the Room and Rounding Up:**
Firstly, convert the area from square feet to square yards:
\[ \text{Area](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25d3b930-d5b3-4b00-b8c4-4be4bbb818dd%2F1fd76161-674a-495d-be87-220607d09508%2F1y5v9pi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Given:**
A rectangular room measures 13 feet by 15 feet. It is going to be carpeted with carpeting that sells for $68 per square yard.
**Questions:**
a. What is the area of the room in square feet?
b. If the scale of the room drawing is 1/4 inch = 1 foot, give the dimensions of the room in inches on the scale drawing.
c. A yard equals 3 feet. How many square feet are in a square yard?
d. How many square yards will it take to carpet the room? Round up to the next greater integer.
### Solutions:
**a. Calculating the Area of the Room in Square Feet:**
To find the area in square feet:
\[ \text{Area} = \text{Length} \times \text{Width} \]
\[ \text{Area} = 13 \, \text{ft} \times 15 \, \text{ft} \]
\[ \text{Area} = 195 \, \text{square feet} \]
**b. Converting Room Dimensions to Scale Drawing Dimensions:**
Given the scale: 1/4 inch = 1 foot, we convert the room dimensions to inches.
\[ \text{Length in inches} = 13 \, \text{ft} \times \frac{1}{4} \, \text{inch/ft} = 3.25 \, \text{inches} \]
\[ \text{Width in inches} = 15 \, \text{ft} \times \frac{1}{4} \, \text{inch/ft} = 3.75 \, \text{inches} \]
So, the dimensions of the room on the scale drawing are 3.25 inches by 3.75 inches.
**c. Calculating Square Feet in a Square Yard:**
A yard equals 3 feet, so:
\[ \text{1 Square Yard} = \left(3 \, \text{ft} \times 3 \, \text{ft}\right) \]
\[ \text{1 Square Yard} = 9 \, \text{square feet} \]
**d. Calculating Square Yards Needed to Carpet the Room and Rounding Up:**
Firstly, convert the area from square feet to square yards:
\[ \text{Area
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