Question

Zoey is covering a 14-inch-square board with 1-inch-square tiles. She uses gray tiles to make three 3-in. by 3-in. squares on the board. She covers the rest of the board with white tiles.

How many more white tiles than gray tiles will Zoey use?

Answer 1

`142\ tiles`

Explanation:

step 1

Find the total tiles in the square board

The total area of the square board is equal to

`A=14^(2)=196\ in^(2)`

Remember that each tile is 1-inch-square

so

by proportion

The total tiles is equal to

`196\ tiles`

step 2

Find the number of gray tiles in the square board

The total area of gray tiles in the square board is equal to

`A=3[(3)(3)]=27\ in^(2)`

Remember that each tile is 1-inch-square

so

by proportion

The total gray tiles is equal to

`27\ tiles`

step 3

Find the number of white tiles in the square board

Subtract the number of gray tiles from the total number of tiles

`196-27=169\ tiles`

step 4

Find out how more white tiles than gray tiles will Zoey use

Subtract the number of gray tiles from the number of white tiles

`169-27=142\ tiles`