Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 10 - Geometry - Chapter Summary, Review, and Test - Review Exercises - Page 682: 47


Total cost = $\$787.50$

Work Step by Step

To find the total cost, there is a need to know the area of the rectangular floor. The area of a rectangle is given by the formula $A=lw$ where l = length and w = width. The floor has a length of 21 feet and a width of 15 feet. Solve for the area of the floor to obtain: $A= lw \\A = 21(15) \\A= 315 \text{ square feet}$ Each square yard of carpet costs $\$22.50$. Each yard is equivalent to 3 feet. Thus, 1 square yard = $3(3) = 9 \text{ square feet}$. This means that 9 square feet of carpet costs $\$22.50$. Solve for the cost of each square foot of carpet by dividing the cost per square yard by $9$: $\text{cost of carpet per square foot} = \dfrac{\$22.50}{9}=\$2.50$ Multiply the cost of the carpet per square foot to the area of the floor to obtain: Total cost = $\$2.50(315) = \$787.50$
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