Question

use the diagram to solve each problem. show your work. 1. how many square feet of carpet does henry need to carpet this room? 2. the carpet henry 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. henry wants to put a pad under the carpet. it costs $3 per square yard. how much will the pad cost?

Explanation:

Step1: Divide the room into rectangles

We can divide the room into two rectangles. One rectangle has dimensions 22 ft by 8 ft and the other has dimensions 27 ft by 5 ft.

Step2: Calculate the area of the first rectangle

The area formula for a rectangle is $A = l\times w$. For the first rectangle with $l = 22$ ft and $w = 8$ ft, $A_1=22\times8 = 176$ square - feet.

Step3: Calculate the area of the second rectangle

For the second rectangle with $l = 27$ ft and $w = 5$ ft, $A_2=27\times5 = 135$ square - feet.

Step4: Find the total area of the room in square - feet

The total area $A = A_1+A_2$. So, $A=176 + 135=311$ square - feet. This answers question 1.

Step5: Convert the area from square - feet to square - yards

Since 1 square yard = 9 square feet, the area in square yards is $A_y=\frac{311}{9}\approx34.56$ square yards.

Step6: Calculate the cost of the carpet

The carpet costs $20 per square yard. So the cost of the carpet $C_{carpet}=20\times\frac{311}{9}=\frac{6220}{9}\approx691.11$ dollars. This answers question 2.

Step7: Calculate the cost of the pad

The pad costs $3 per square yard. So the cost of the pad $C_{pad}=3\times\frac{311}{9}=\frac{311}{3}\approx103.67$ dollars. This answers question 3.

Answer:

1. 311 square feet
2. Approximately $\$691.11$
3. Approximately $\$103.67$