Solving word problems

Question

The perimeter of a rectangular wooden deck is 90 feet. The deck's length, I, is 5 feet less than 4 times its width, w, Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?

Answer 1

The Perimeter is 90 feet, so:

(2L) + (2W) = 90

The Length is 5 feet less than 4 times its Width, so:

L = 4W - 5

The system of equations is:

2L + 2W = 90

L = 4W - 5

Replacing L in the first equation:

(2L) + (2W) = 90

2 (4W - 5) + 2W = 90

8W - 10 + 2W = 90

10W = 90 + 10

10W = 100

W = 100 / 10

W = 10

Replacing W in the second equation:

L = 4W - 5

L = 4 • 10 - 5

L = 40 - 5

L = 35

The Length is 35 feet and the Width is 10 feet.