SOLUTION: a 140-second song is divided into three parts, the begining, the middle, and the end. the beginning is one-sixth as long as the end. the middle is one half as long as the end. find

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Question 339026: a 140-second song is divided into three parts, the begining, the middle, and the end. the beginning is one-sixth as long as the end. the middle is one half as long as the end. find the length of each part
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let beginning = b
Let middle = m
Let end = e
given:
(1) b+%2B+m+%2B+e+=+140
(2) b+=+%281%2F6%29%2Ae
(3) m+=+%281%2F2%29%2Ae
-----------------
There are 3 unknowns and 3 equations, so
it should be solvable
Substitutute (2) in (1)
(1) %281%2F6%29%2Ae+%2B+m+%2B+e+=+140
Substitute (3) in (1)
(1) %281%2F6%29%2Ae+%2B+%281%2F2%29%2Ae+%2B+e+=+140
Multiply both sides by 6
(1) e+%2B+3e+%2B+6e+=+840
10e+=+840
e+=+84
And, from (2)
b+=+%281%2F6%29%2A84
b+=+14
From (3)
m+=+%281%2F2%29%2A84
m+=+42
The beginning is 14 min
The middle is 42 min
The end is 84 min
check:
(1) b+%2B+m+%2B+e+=+140
14+%2B+42+%2B+84+=+140
140+=+140
(2) b+=+%281%2F6%29%2Ae
(2) b+=+%281%2F6%29%2A84
14+=+84%2F6
14+=+14
(3) m+=+%281%2F2%29%2Ae
(3) 42+=+%281%2F2%29%2A84
42+=+42
OK