Arthur is putting a tile floor in this room. The tiles are 1 foot on each side. Half of the tiles will be dark brown tiles that cost 58 cents each. The other half will be light brown tiles that are on sale for 49 cents each. How much will the tiles for this floor cost? The Floor is 17x8

Hey. Let me help you on this one.

As the question says, the area of the floor surface is 17 feet by 9 feet. Each floor tile is 1 foot in length, and 1 foot in width. We know that the area of one tile is [tex]1^{2} [/tex]ft squared if we substitute numbers into the square area formula and solve it.

[tex]S=a*b[/tex]
[tex]S=1*1[/tex]
[tex]S=1[/tex]

We understand that each tile costs a different amount of money, so that's why we need to set up an equation we can later solve. For this; however, we will need to know the complete area of the floor since this is going to be our total.

In order for us to solve for the total area, we have to use the same area formula we used a step ago.

Length of the floor is 17 feet, while the width is 8 feet. Let's multiply them together.

[tex]S=a*b[/tex]
[tex]S=17*8[/tex]
[tex]S=136[/tex]

Awesome! We know the complete area of the floor as the whole, which is 136 feet squared, and area of the individual tile is 1 foot squared.

If we divide 136 by 1, we will determine the amount of square tiles within the floor. 136 divided by 1 is 136, meaning that there are 136 tiles in the floor.

Now, let's form the solution that will show both prices and amounts of the tiles. Our first initial step is to find out how much one half of 136 is. We can do it by finding 50% of 136.

[tex]0.5*136=68[/tex]

One half of 136 is 68, meaning that 68 tiles will cost 58 cents each, and that other 68 tiles will cost 49 cents each. Let's form the solution which we can then solve.

[tex](68*58)+(68*49)[/tex]
[tex]3944+3332=7276[/tex]

Answer: 7276 cents, or $72.76 is the price of the floor.