hennaj wrote:

A certain rectangular wall is 12 feet high and 8 feet long. It will be tiled with nonoverlapping square tiles that have sides of length 16 inches. The entire wall will be covered with tile and no tiles will be cut. Each tile consists of 16 smaller squares, each with sides of length 4 inches in the pattern shown in the diagram above. How many small blue squares will be on the wall? (1ft = 12 in)

a. 24

b. 216

c. 288

d. 864

e. 1,152

Distraction: "Each tile consists of 16 smaller squares, each with sides of length 4 inches . . ."

We already know that "each tile" has the pattern in the diagram, that is, each large tile (16 in. by 16 in.) has 4 blue tiles.

So we find the number of 16 by 16 tiles that will fit into the area of the wall, and multiply that number by 4 to get the number of blue tiles.

I converted and divided the way I did to avoid huge numbers.*

1) Convert feet to inches for wall height and length

Wall height = 12 feet = 12 feet * 12 inches/foot = 144 inches

Wall length = 8 feet * 12 inches/foot = 96 inches

2)Calculate how many tiles will fit: Divide height and length of wall, respectively, by length of one side of a tile

Length of

one side of a tile = 16 inches

So the height will have 144 in/16 in = 9 tiles (that will form 9 rows)

Length will have 96 in/16 in = 6 tiles (that will form 6 columns)

Total number of tiles is 9 * 6 = 54 tiles

3) How many blue tiles total?

There are 4 blue tiles on one big tile. 4 blue tiles * 54 big tiles = 216 blue tiles

Answer B

*I did not use these calculations when doing the problem, but here is the arithmetic with no "shortcuts":

Wall area (where 12 feet = 144 inches and 8 feet = 96 inches) --> 144 in * 96 in = 13,284 sq in

Tile area = 16 in * 16 in = 256 sq in

Wall area/tile area = # of tiles that will fit

13,284 sq in/256 sq in per tile = 54 tiles

54 tiles * 4 blue per tile = 216 blue