Question

Aiden is replacing the tile in a rectangular kitchen. The length of the kitchen is nine feet shorter than three times its width, w. The perimeter of the kitchen is six times the width. If tiles cost $1.69 a square foot, what is the total cost to tile the kitchen?

Answer 1

Answer:

Total Cost to tile = $273.28

Let x be the Width; then

3x - 9 = Length; hence

2(W + L) = Perimeter; therefore

6x = 2(x + 3x - 9)

6x = 2(4x - 9) = 8x - 18

6x - 8x = -18

-2x = -18

x = 9

Width = x = 9 ft

Length = 3x - 9 = 3 times 9, minus 9 = 27 - 9 = 18 ft

Area = W times L = 9 ft. times 18 ft. = 162 sq. ft.

Cost of Tile = $1.69 per sq. ft.

Total Cost = $1.69 times 162 = $273.28

To check:

Perimeter = 6(W) = 6x = 6 times 9 ft. = 54 ft.; also

Perimeter = 2(W + L) = 2(9 + 18) = 2(27) = 54 ft