A 14 -foot piece of string is cut into two pieces so that the longer piece is 2 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

X = shorter piece

y = longer piece

x + y = 14

y = 2x + 2

x + (2x + 2) = 14

3x + 2 = 14

3x = 14 - 2

3x = 12

x = 12/3

x = 4 ... shorter piece (x) is 4 ft

y = 2x + 2

y = 2 (4) + 2

y = 8 + 2

y = 10 ... longer piece (y) is 10 ft

We are given that the shorter piece is x

From your description, the longer piece is 2x + 2

The total length is

x + 2x + 2 = 14

ie

3x + 2 = 14

3x = 12

x = 4

So the length of the shorter piece is 4 ft

Therefore the length of the longer piece must be

(14 - 4) ft = 10 ft