Question

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?

Answer 1

Answer:

$C = 495 + 13.05x$

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  

$C = (550 + 14.5x)(1 - \frac{10}{100}) = 495 + 13.05x$ .......... (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)