SOLUTION: A wire 180 centimeters long is to be cut into three pieces. The length of one piece is three times the length of the second. The length of the third piece is 12 centimeters shorter

Click here to see ALL problems on Length-and-distance

Question 314761: A wire 180 centimeters long is to be cut into three pieces. The length of one piece is three times the length of the second. The length of the third piece is 12 centimeters shorter than twice the length of the second. Find the length of each piece.
Found 2 solutions by Jstrasner, mananth:
Answer by Jstrasner(112) (Show Source):
You can put this solution on YOUR website!
Hey,
Let's write down what we know:
p1 + p2 + p3 = 180 cm
p1 = 3*(p2)
p2 = 12 + p3
Now we can substitute:
p1 = 3*(12 + p3) => 36 +3p3
We can then take this into the original equation to find out what the length of p3 is:
36 + 3p3 + 12 + p3 + p3 = 180
48 + 5p3 = 180
5p3 = 132
p3 = 26.4 cm
then we put this into the other equation:
p2 = 26.4 + 12 => 38.4
and then we put these into the other equation:
p1 = 3*38.4 => 115.2
Therefore:
p1 = 115.2 cm
p2 = 38.4cm
p3 = 26.4cm
I hope this helps!

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
get the lengths of the 3 pieces in terms of x
let second piece be x
the first will be 3x
the third will be 2x-12
..
add all
x+3x+2x-12=180
6x-12=180
6x=192
x=32 cm second piece
first piece = 3x = 96 first piece
third piece 2x-12= 64-12 = 52.
CHECK
32+96+52= 180