Amanda is having new tile installed in her kitchen. TileAll charges a flat fee of $378.00 plus $15.00 per tile. KitchenPlus charges a flat fee of $550.00 plus $14.50 per tile. Amanda has a 10% discount coupon at KitchenPlus. If Amanda purchases x tiles, the following expression can be used to model the average cost per tile at KitchenPlus.
How many tiles does Amanda have to order for the average cost per tile to be equal at both TileAll and KitchenPlus?

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240