Question

to move forward with the renovations, your aunt needs to approve your costs to make sure that you do not go over the $800.00 budget for the shower.

1. cost of the tile needed.

a. calculate the surface area of all of the rectangles that will need to be covered in tile.
b. calculate the number of tiles needed. remember the tiles that are being used are 10 cm x 10 cm. hint: you will need to calculate the surface area for one tile first.
c. calculate the total cost for the tiles. remember that each tile costs $0.40.

Explanation:

Step1: Calculate area of one tile

The area of a square - shaped tile with side length $s = 10$ cm is $A_{tile}=s\times s$. Since $s = 10$ cm, $A_{tile}=10\times10 = 100$ $cm^{2}$.

Step2: Assume surface area to be covered is $A_{total}$ (not given in the problem - let's assume it for the sake of showing the process). Let $A_{total}=x$ $cm^{2}$

The number of tiles $n=\frac{A_{total}}{A_{tile}}=\frac{x}{100}$.

Step3: Calculate total cost

Since each tile costs $0.40$ dollars, the total cost $C = 0.40\times n$. Substituting $n=\frac{x}{100}$ into the cost formula, we get $C=0.40\times\frac{x}{100}=\frac{0.4x}{100}=0.004x$ dollars.

However, since the actual surface - area to be covered ($A_{total}$) is not given in the problem, we can't give a numerical answer. If we had the value of the surface area of the rectangles to be covered in $cm^{2}$, we could follow these steps to get the answer.

If we assume the surface area of the rectangles to be covered is $A_{total} = 5000$ $cm^{2}$:

Step1: Calculate area of one tile

$A_{tile}=10\times10 = 100$ $cm^{2}$

Step2: Calculate number of tiles

$n=\frac{5000}{100}=50$

Step3: Calculate total cost

$C = 0.40\times50=20$ dollars

Answer:

If the surface area of the rectangles to be covered is $5000$ $cm^{2}$, the total cost of the tiles is $20$ dollars. Without knowing the actual surface area of the rectangles to be covered, we can't give a definite numerical answer. The general formula for the total cost $C$ in terms of the surface area to be covered $A_{total}$ (in $cm^{2}$) is $C = 0.004A_{total}$ dollars.