Question

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?

Answer 1

Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:

x + 2y = 29

Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:

x = 2y + 1

Substituting this expression for x in the first equation, we get:

2y + 1 + 2y = 29

Combining like terms on both sides, we get:

4y + 1 = 29

Subtracting 1 from both sides, we get:

4y = 28

Dividing both sides by 4, we get:

y = 7

Substituting this value for y in the expression for x, we get:

x = 2(7) + 1 = 14 + 1 = 15

Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.