A 16 foot board is cut into three lengths where the first length is x, the second piece is 3 feet less than twice the first and third piece is 2 feet more than the second.

Question

A 16 foot board is cut into three lengths where the first length is x, the second piece is 3 feet less than twice the first and third piece is 2 feet more than the second.Find the length of the shortest piece

Answer 1

First, assign variables: Call the three lengths x, y, and z. x is the 1st board

Using the description:

y = 2x - 3

z = y + 3

finally, we have x + y + z = 16

We now have three equations and three unknowns, so we can solve it.

Answer 2

Let's define the length of the 3 boards in terms of x:

1st board: x

2nd board: 2x - 3

3rd board: (2x - 3) + 2

Now we add them all up and set the sum equal to 16:

x + 2x - 3 + 2x - 3 + 2 = 16

5x - 4 = 16

5x = 20

x = 4 ft