Question

the home cleaning company charges $312 to power-wash the siding of the house plus $12 for each window. power clean charges $36 per window, and the price includes power -washing the siding. how many windows must a house have to make the total cost from the home cleaning company more expensive than power clean? let w be the number of windows. (creating and solving

Answer 1

To find the number of windows required for the total cost from the home cleaning company to be more expensive than Power Clean, set up and solve an inequality. The house must have more than 26 windows in order for the total cost from the home cleaning company to be more expensive than Power Clean.

Step-by-step explanation:

To determine the number of windows required for the total cost from the home cleaning company to be more expensive than Power Clean, we need to set up an inequality.

The total cost from the home cleaning company is $312 for power-washing the siding plus $12 for each window, so the total cost is given by the equation 312 + 12w, where w is the number of windows.

The total cost from Power Clean is $36 per window, so the total cost is given by the equation 36w.

To find the point at which the total cost from the home cleaning company becomes more expensive than Power Clean, we need to set up the inequality 312 + 12w > 36w. Simplifying this inequality gives us w > 26.

Therefore, the house must have more than 26 windows in order for the total cost from the home cleaning company to be more expensive than Power Clean.

Answer 2

$312 to power-wash + $12 /w

power clean $36/w

Ok

312 + 12w > 36w

312 > 36w - 12w

312 > 24w

312/24 > W

13 > w

13 windows, let's check

312 + 12w > 36w

312 + 12(13) > 36(13)

312 + 156 > 468

468 > 468 with 13 windows the cost is the same

then, use 14 windows

312 + 12(14) > 36(14)

312 + 168 > 504

480

The answer is 12 windows

312 + 12(12) > 36(12)

312 + 144 > 432

456 > 432 12 windows