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 single tile with dimensions \(10\ cm\times10\ cm\) is \(A_{tile}=10\times10 = 100\ cm^{2}\) or \(0.01\ m^{2}\) (since \(1\ m = 100\ cm\), \(1\ cm^{2}=\frac{1}{10000}\ m^{2}\)). However, we'll work in \(cm^{2}\) for now. But we first need to know the total area to be tiled. Let's assume the total area of the rectangles to be tiled is \(A_{total}\ cm^{2}\). Since this value is not given in the problem - statement, we'll continue with the general formula.

Step2: Calculate number of tiles

The number of tiles \(n=\frac{A_{total}}{A_{tile}}=\frac{A_{total}}{100}\) (in \(cm^{2}\)).

Step3: Calculate total cost

The cost of each tile is \(C_{per - tile}=\$0.40\). The total cost \(C = n\times C_{per - tile}=\frac{A_{total}}{100}\times0.40=\frac{0.4A_{total}}{100}= 0.004A_{total}\) (in dollars).

Since the total area \(A_{total}\) of the rectangles to be tiled is not given, we can't give a numerical answer. But if we had the value of \(A_{total}\) (in \(cm^{2}\)), we could substitute it into the formula for the total cost.

If we assume the total area of the rectangles to be tiled \(A_{total} = x\ cm^{2}\):

Answer:

The number of tiles \(n=\frac{x}{100}\) and the total cost \(C = 0.004x\) dollars.