Question

26. A rectangular piece of carpet is placed on the floor of a room leavinga margin of 1 yd around it. The room measures 7 yd by 6 yd. Find thecost of the carpet if 1 yd^2 of it costs $75.I was looking for answer worked out with each step

Answer 1

$1500

Explanation

the area of a rectangle is given by:

$\text{Area}_{rec\tan gle}=length\cdot width$

Step 1

Let

$\begin{gathered} \text{length of carpet= legth of the room-2(1yd)} \\ \text{widht of carpet=width of the room -2(1 yd)} \\ \end{gathered}$

so, replacing

$\begin{gathered} \text{length of carpet= 7yd-2yd}=5\text{ yd} \\ \text{widht of carpet=6 yd -2 yd = 4 yd} \\ \end{gathered}$

so,the area of the carpet is

$\begin{gathered} \text{Area}_{rec\tan gle}=length\cdot width \\ \text{Area}_{carpet}=5\text{ yd }\cdot4\text{ yd} \\ \text{Area}_{carpet}=20(yd^2) \end{gathered}$

Step 2

find the cost of the carpet.

to find the total cost just multipy the area by the cost per square yard, so

$\begin{gathered} \text{Cost}_{carpet}=20(yd^2)\cdot\text{ 75}\frac{\text{ \ }}{yd^2} \\ \text{Cost}_{carpet}=1500 \end{gathered}$

so,the cost is $1500

I hope this helps you