Question

Margo can purchase tile at a store for $0.99 per tile and rent a tile saw for $12. 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?

a) 12 tiles
b) 20 tiles
c) 18 tiles
d) 14 tiles

Answer 1

Margo must buy 30 tiles for the cost of purchasing them and renting or borrowing a tile saw to be the same at both stores, after solving the equations Cost1 = 0.99x + 12 and Cost2 = 1.39x.

Step-by-step explanation:

The student is tasked with finding the point at which the cost of buying tiles and renting or borrowing a saw from two different stores is the same. We set up two equations representing the cost from each store and solve for the number of tiles purchased where the costs are equal.

Let x be the number of tiles Margo buys. At the first store, the cost is $0.99 per tile plus a $12 saw rental. This gives us the equation Cost1 = 0.99x + 12. At the second store, the cost is $1.39 per tile with a free saw rental, giving us the equation Cost2 = 1.39x.

Now we set the two costs equal to each other to find the number of tiles where Margo spends the same amount at both stores:

0.99x + 12 = 1.39x

Subtract 0.99x from both sides to get:

12 = 0.40x

And then divide both sides by 0.40 to solve for x:

x = 30 tiles

Therefore, Margo must buy 30 tiles for the cost to be the same at both stores.