Question

Margo can purchase tile at a store for $0.79 per tile and rent a tile saw for $18. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?

Answer 1

30 tiles

Explanation:

We write a cost function for each store. Then we set the cost functions equal and solve for x, the number of tiles.

Let x = number of tiles.

cost = fixed cost (saw rental) + cost per tile

First store:

saw rental = $18

cost per tile: $0.79

cost of x tiles: 0.79x

cost function:

c(x) = 0.79x + 18

Second store:

saw rental = $0

cost per tile: $1.39

cost of x tiles: 1.39x

cost function:

c(x) = 1.39x + 0

c(x) = 1.39x

Now we set the cost functions equal and solve for x.

1.39x = 0.79x + 18

Subtract 0.79x from both sides.

0.6x = 18

Divide both sides by 0.6

x = 18/0.6

x = 30

Answer: 30 tiles