If a 16 foot piece of string is cut into 2 pieces so that the longer piece is 1 foot longer that twice the shorter piece if the shorter piece is x foot long, find the length of both pieces

Well,

We can write everything down based on x.

Longer piece = 2x + 1

Longer piece + Shorter piece = 16

x + 2x + 1 = 16

Collect Like Terms

3x + 1 = 16

Subtract 1 from both sides

3x = 15

Divide both sides by 3

x = 5

Longer piece = 2x + 1

Longer piece = 2 (5) + 1

Longer piece = 10 + 1

Longer piece = 11

11 + 5 = 16

Longer piece = 11 ft.

Shorter piece = 5 ft.