Mr. Lings has a plank of wood 118 inches long. He cuts it into two pieces such that the longer piece is 5.5 inches longer than twice the length of the shorter piece. What is the length of the longer piece?

Length: 80.5 inches; width: 37.5 inches

Step-by-step explanation:

Let L represent the length of the longer piece, and

S represent the length of the shorter piece.

L + S = 118 inches.

(2S + 5.5 inches) + S = 118 inches

Combining like terms, we get 3S + 5.5 inches = 118 inches, or (after subtracting 5.5 inches from both sides)

3S = 112.5

Dividing both sides by 3 gives us a formula for S:

S = 112.5 inches/3 = 37.5 inches

The shorter piece has length 37.5 inches, and the longer piece 80.5 inches.

Note that 2 (37.5 inches) + 5.5 inches = 80.5 inches. So these results check out well.