SOLUTION: A 14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.

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Question 75996This question is from textbook
: A 14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece. This question is from textbook

Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Let x=length of shorter piece
And y=longer piece
Now we are told that:
x+y=14-----------------------------------eq 1
We are also told that:
3y=4x---------------------------------------eq 2
divide both sides of eq 2 by 3 and we get:
y=(4/3)x---substitute this into eq 1:
x+(4/3)x=14 or
(7/3)x=14 multiply both sides by 3
7x=42 divide both sides by 7
x=6 yards------------------------------shorter piece
Substitute x=6 into eq 1:
6+y=14 subtract 6 from both sides
y=8 yards----------------------------------longer piece
Ck
6+8=14
14=14
and
3 times longer = 4 times shorter or
3*8=4*6
24=24

Hope this helps---ptaylor