Question

A 32 ft board is cut into three pieces at a sawmill. The second piece is 5 ft longer than the first and the third piece is 1 ft longer than the second.

What are the lengths of the three pieces?

Answer 1

The first piece is 7 ft long, the second piece is 12 ft long, and the third piece is 13 ft long

Explanation:

Let x represent the length of the first piece.

Since the second piece is 5 ft longer than the first, it can be represented by x + 5

Since the third piece is 1 ft longer than the second, it can be represented by x + 6

Create an equation that adds all of these terms up to 32, and solve for x

(x) + (x + 5) + (x + 6) = 32

3x + 11 = 32

3x = 21

x = 7

So, the first piece is 7 ft long.

Using the expressions we created, solve for the lengths of the second and third pieces.

x + 5

7 + 5 = 12

x + 6

7 + 6 = 13

The first piece is 7 ft long, the second piece is 12 ft long, and the third piece is 13 ft long