# A carpenter used 29 ft of molding in three pieces to trim a garage door. If the long piece was 1 ft longer than twice the length of each shorter piece, then how long was each piece?

Dec 3, 2016

Each of the shorter pieces was $7 f t$ and the long piece was $15 f t$.

#### Explanation:

If we represent each of the shorter pieces by $x$, then the long piece can be represented as $\left(2 x + 1\right)$.

Since there are two short pieces, we can write an equation:

$x + x + \left(2 x + 1\right) = 29$

Open the brackets and simplify.

$x + x + 2 x + 1 = 29$

$4 x + 1 = 29$

Subtract $1$ from each side.

$4 x = 28$

Divide both sides by $7$.

$x = 7$

$\therefore \left(2 x + 1\right) = 15$