Number of tiles needed?

My approach:

We know that each design uses 3 "L" tiles. If we can figure out how many designs it will take to cover the whole floor, we can multiply that by 3 to find the number of "L" tiles needed.

The only thing to be careful about is that we use consistent units. The design is 8*8 square inches, and the floor area is 10*12 feet, or (10*12) * (12*12) square inches (remember 1 foot = 12 inches).

Let's find the number of full designs needed by dividing the total area by the area of each design:


Notice that when solving a problem that requires many multiplications and divisions, I try to simplify numbers as much as I can before I perform multiplications; this keeps the numbers as small as possible and allows me to work faster.

-Patrick

gmattesttaker2 wrote: The figure above shows a large square formed by fitting three L-shaped tiles and one small square tile together. If a rectangular floor l0 feet by 12 feet is to be tiled in large squares of this design, how many L-shaped tiles will be needed?

The approach below employs the following conversion rates:
3 L-tiles = (8 inches)(8 inches) = 64 square inches.
1 square foot = (1 foot)(1 foot) = (12 inches)(12 inches) = 144 square inches.
1 floor = (10 feet)(12 feet) = 120 square feet.

In the product below, all of the colored units CANCEL OUT, leaving the resulting values in terms of L-TILES PER FLOOR:
(3 L-tiles)/(64 square inches) * (144 square inches)/(1 square foot) * (120 square feet)/(1 floor)

= (3*144*120)/(8*8)

= 3*18*15

= 810 L-tiles per floor.