A19-foot piece of string is cut into two pieces so that the longer piece is 4 feet longer than twice the shorter piece. if the shorter piece is x feet long find the lengths of both peices

Here, 
let the longer piece be y and shorter piece be x
now,
according to the question,
x+y=19     equation (1)
y=4+2x    equation (2)

from equation 1
x+y=19
x+4+2x=19          substituting the value of y from equation 2
3x=19-4
x=(19-4)/3
x=5

now 
substituting value of x in equation (2)
y=4+2(5)
y=4+10
y=14

so , the longer piece is 14 foot and the shorter piece is 5 foot

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