Danny wants to have his bathroom floor re-tiled. The dimensions of the floor are (3x+1) by (2x+1). Write a quadratic expression that represents the area of the floor. If x=1m, what is the area that needs to be re-tiled? The tiles cost $5/m^2. How much will it cost Danny to re-tile his floor?
The area of the floor can be represented by the quadratic expression:
Area = (3x+1)(2x+1)
Area = 6x^2 + 3x + 2x + 1
Area = 6x^2 + 5x + 1
Plugging in x=1m:
Area = 6(1)^2 + 5(1) + 1
Area = 6 + 5 + 1
Area = 12 square meters
So, Danny will need to re-tile an area of 12 square meters.
The cost of re-tiling the floor is given by multiplying the area by the cost of tiles:
Cost = Area * Cost per square meter
Cost = 12 * $5
Cost = $60
It will cost Danny $60 to re-tile his bathroom floor.