Question 851476
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.