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 . . ."
Focus instead on the 16x16 tiles.-- "each [large 16x16] tile" per the pattern in the diagram, has 4 smaller blue tiles.
-- find the number of large (16x16) tiles that will fit into the area of the wall. 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/1foot = 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
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