How many square feet of each tile should he plan to use if he wants the overall cost to be $4.72 per square foot?

Question

Sergio wants to tile the floor of his house. He will need  square feet of tile. He will do most of the floor with a tile that costs  per square foot, but also wants to use an accent tile that costs  per square foot. How many square feet of each tile should he plan to use if he wants the overall cost to be  per square foot? 

Answer 1

Hi Jeralyn,

There are many ways to solve this problem, but since you indicated Algebra 2, we will use the system of linear equations.

Let us denote the area tiled with regular tiles R, and the area tiled with accent tiles A.

R + A = 755 (the total tiled area is 755 sq. ft.)

3.2 R + 10.15 A = 755 x 4.72 = 3,563.6 (the total cost should be equal to 755 sq. ft. x $4.72 per sq. ft.)

Now let us solve the system of equations.

First let us multiply both sides of the first equation by 3.2

We will get

3.2 R + 3.2 A = 2,416 (this is the cost of covering the whole house with regular tile)

Now let us subtract this equation from the second equation.

We will get

6.95 A = 1,147.6 (the extra costs due to the accent tiles)

Now we can solve for A

A = 1,147.6 / 6.95 ≈ 165 (square feet of accent tile)

And after substituting A into the first equation

R + 165 = 755

We can solve for R

R = 755 - 165 = 590 (square feet of regular tile)

Now we have our answer: Sergio needs to use 590 sq. ft. of regular tile and 165 sq. ft. of accent tile.

Answer 2

x represents the amount of tile for most of the floor

755 - x represents the amount of tile for the trim.

3.20x + 10.15(755 - x) = 4.72(755)

Can you solve for x and answer?