Question

use the diagram to solve each problem. show your work. 1. how many square feet of carpeting does dena need to carpet this room? 2. the carpet dena wants to buy costs $20 per square yard. how much will the carpet cost for this room? (hint: 1 square yard = 9 square feet) 3. dena wants to put a pad under the carpet. it costs $3 per square yard. how much will the pad cost?

Explanation:

Step1: Calculate the area of the room in square - feet

The room can be thought of as a large rectangle with a smaller rectangle cut out. The area of the large rectangle with length 20 ft and width 15 ft is $A_{1}=20\times15 = 300$ square - feet. The area of the smaller rectangle (the cut - out part) with length $(20 - 15)=5$ ft and width 5 ft is $A_{2}=5\times5 = 25$ square - feet. The area of the room $A = A_{1}-A_{2}=300 - 25=275$ square - feet.

Step2: Convert the area from square - feet to square - yards for question 2 and 3

Since 1 square yard = 9 square feet, the area of the room in square yards is $A_{yd}=\frac{275}{9}\approx30.56$ square yards.

Step3: Calculate the cost of the carpet

The carpet costs $20 per square yard. So the cost of the carpet $C_{carpet}=20\times\frac{275}{9}=\frac{5500}{9}\approx611.11$ dollars.

Step4: Calculate the cost of the pad

The pad costs $3 per square yard. So the cost of the pad $C_{pad}=3\times\frac{275}{9}=\frac{275}{3}\approx91.67$ dollars.

Answer:

1. 275 square feet
2. $\frac{5500}{9}\approx611.11$ dollars
3. $\frac{275}{3}\approx91.67$ dollars