Question

5 ft 4 ft Mila and her mom are tiling the playroom floor with two colors of tiles. They have 70 dark gray tiles and 30 light gray tiles. Each tile is 1 square foot. The diagram shows Mila's plan. 8 ft light gray а. Show how to find the total area that they are tiling. b. Will Mila's plan work with the tiles she has? Explain.

Answer 1

Part a.

The total area is the area of the rectangle, that is,

which is the wide times the lenght. So, the total area is

`A=8*9=72ft^2`

Part b.

We need to find the dark gray area and the light gray area separately. The dark gray area is

`A_{\text{dark}}=8*5=40ft^2`

and the light gray area is

`A_{\text{light}}=8*4=32ft^2`

In the first case, Mila has 70 dark gray tiles, since each tile is 1 square foot, she has 70 square foot of tiles then, in this particular case, her plan will work because the dark area is 40 square feet. However, in the light gray case, she only has 30 tiles or, equivalently, 30 square foot of tiles but the light gray area is 32 square feet, so she will need 2 more tiles. Therefore, her plan doesnt quite work.