A 23-foot board is cut into two pieces. Twice the length of the shorter piece is 4 ft more than the length of the longer piece. Find the length of the shorter piece.

Answer 1

Let's call the two lengths S and L (for short and long).

S + L = 23 (together they make 23 feet)

2S = L- 4 (Twice the length of the shorter is equal to the longer minus 4 feet).

S + L = 23 can be re-written as S = 23 - L

Since you cannot solve an equation with two variables, we'll use first equation to replace part of the second.

2(23 - L) = L - 4

Distribute the 2: 46 - 2L = L - 4

Add 4 to both sides: 50 - 2L = L

Add 2L to both sides: 50 = 3L

Divide both sides by 3: L = 16 2/3

So the longer piece is 16 2/3 feet.

Now plug that back into the original equation: S + L = 23.

S + 16 2/3 = 23

Subtract 16 2/3 from both sides: S = 6 1/3

The shorter piece is 6 1/3 feet.