SOLUTION: Divide 150 into three parts such that the second number is five-sixths the first and the third number is four-fifths the second.

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Question 630286: Divide 150 into three parts such that the second number is five-sixths the first and the third number is four-fifths the second.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the 3 parts be a, b, and c
given:
(1) +a+%2B+b+%2B+c+=+150+
(2) +b+=+%285%2F6%29%2Aa+
(3) +c+=+%284%2F5%29%2Ab+
----------------
(2) +a+=+%286%2F5%29%2Ab+
Substitute (2) and (3) into (1)
(1) +%286%2F5%29%2Ab+%2B+b+%2B+%284%2F5%29%2Ab+=+150+
(1) +b%2A%28+6%2F5+%2B+5%2F5+%2B+4%2F5+%29+=+150+
Multiply both sides by +5+
(1) +b%2A%28+6+%2B+5+%2B+4+%29+=+750+
(1) +b+=+750+%2F+15+
(1) +b+=+50++
and, since
(3) +c+=+%284%2F5%29%2Ab+
(3) +c+=+%284%2F5%29%2A50+
(3) +c+=+40+
and
(2) +a+=+%286%2F5%29%2Ab+
(2) +a+=+%286%2F5%29%2A50+
(20 +a+=+60+
The lengths are 60, 50, and 40