SOLUTION: a-1 Carpet charges $150 to remove old carpet,and $20 per square yard for new carpeting. Ruggs carpet company only charges $80 to remove old carpet,but $22 per square yard for new c

Question 851476: a-1 Carpet charges $150 to remove old carpet,and $20 per square yard for new carpeting. Ruggs carpet company only charges $80 to remove old carpet,but $22 per square yard for new carpeting. Assuming the quality of the carpet and the work done is the same, how many square yards would yo need to install in order for both companies to be the same cost? What would that cost be? Let y=total cost and let x=square yards of carpet.
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Carpet charges $150 to remove old carpet,and $20 per square yard for new carpeting.
Ruggs carpet company only charges $80 to remove old carpet,but $22 per square yard for new carpeting.
Assuming the quality of the carpet and the work done is the same, how many square yards would you need to install in order for both companies to be the same cost?
What would that cost be? Let y=total cost and let x=square yards of carpet.
Carpet cost:: y1(x) = 150+20x
Ruggs cost:: y2(x) = 80+(22)x
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Equation:
150+20x = 80 + 22x
2x = 70
x = 35 (# of sq. yds. if cost are equal)
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That cost would be 150 + 20*35 = 150 + 700 = $850.00
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Cheers,
Stan H.
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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of square yards of a1 carpet.
y = number of square yards of ruggs carpet.

cost to remove by a1 carpet = 150 + 20x
cost to remove by ruggs carpet = 80 + 22y

if both company costs are the same, then:

150 + 20x = 80 + 22y

solve this equation for y to get:

22y = 150 + 20x - 80
simplify to get:
22y = 70 + 20x

solve for y to get:

y = (70 + 20x) / 22

this equation will calculate the value of y based on the value of x so that the total cost of each option will always be the same.
this is because this equation is based on the cost being equal.
that was the starting point.
150 + 20x = 80 + 22y was the starting point.
this equation said that the cost for a1 carpeting is equal to the cost of ruggs carpeting.
when we solve for y in terms of x, this forced the costs to be equal based on the results of the equation.

there is no one answer to this question.
the value of y depends on the value of x.
the formula will make the cost equal.
for example:
when x = 5, y= 7.7273
cost for a1 carpeting = 150 + 5*20 = 250
cost for ruggs carpeting = 80 + 7.7273*22 = 250
when x = 10, y = 12.273
cost for a1 carpeting = 150 + 10*20 = 350
cost for ruggs carpeting = 80 + 12.273*22 = 350

whatever the value of x is, y becomes a value based on the equation and this causes the total cost for both options to be the same.

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