elementary algebra

[Rani]

Carpeting costs $20 per square yard. You carpet a room that has a width of 15 feet for $800. What is the length of the room in feet?

 

[Someone2841]

Carpeting costs $20 per square yard. You carpet a room that has a width of 15 feet for $800. What is the length of the room in feet?

\(\displaystyle p(x) = \frac{\$20x}{yd^{2}}\) where \(\displaystyle p(x)\) is the price at \(\displaystyle x\) yards of carpet.


We need to solve for \(\displaystyle x\) in terms of \(\displaystyle p\).

\(\displaystyle p(x) = \frac{\$20x}{yd^{2}} \to \frac{yd^{2}}{\$20}p(x) = x\)

Which rewritten as a function of p yields:

\(\displaystyle x(p) = \frac{yd^{2}p}{\$20}\) where \(\displaystyle x(p)\) is the length at \(\displaystyle p\) price.


Now evaluate \(\displaystyle x($800)\)

\(\displaystyle x(\$800) = \frac{yd^{2}\$800}{\$20} = 40yd^{2}\)

 

[Mrspi]

Carpeting costs $20 per square yard. You carpet a room that has a width of 15 feet for $800. What is the length of the room in feet?

If ONE square yard of carpet costs $20 (that's what $20 per square yard means), how many square yards could you buy for $800?

$800/$20 will give you the number of square yards you purchased.

Now, how many square FEET did you buy? I think we want to deal with square feet because the width of the room is 15 feet and the question asks what the length of the room is in feet.

There are 9 square feet in a square yard (a square yard is a square 3 feet on each side, so its area is 3 feet * 3 feet, or 9 square feet).

Take the number of square yards of carpet you purchased, and multiply that by 9 square feet to get the number of square feet you bought. Then remember that the area of a rectangle is length * width.

For your room, the width is 15 feet, and the length is unknown...let's call it x feet. And the area of the room is the number of square feet of carpet you purchased:

length * width = area of room
x * 15 = number of square feet of carpet you bought

Can you finish it yourself now?

 

[mmm4444bot]

Rani:

You are posting on the arithmetic board.

What math course are you in?