Amanda is having new tile installed in her kitchen. tileall charges a flat fee of $378.00 plus $15.00 per tile. kitchen plus 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 kitchen plus.
how many tiles does amanda have to order for the average cost per tile to be equal at both tileall and kitchen plus?

60 tiles.

Step-by-step explanation:

$15.00 per tile plus a flat fee of $378.00 that charges Tile All.

Therefore, for x number of tiles, the total cost of installation will be  

C = 378 + 15x ........... (1)

Again, $14.50 per tiles plus a flat fee of $550.00 that charges Kitchen Plus. Amanda has at Kitchen Plus, a 10% discount coupon.

Therefore, for x tiles installation the charges will be  

.......... (2) (Answer)

Now, if for x number of tiles both the company charges the same, then  

378 + 15x = 495 + 13.05x (From equations (1) and (2)}

⇒ 1.95x = 117

⇒ x = 60 tiles. (Answer)

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: