SOLUTION: divide $1500between a,b and c such that b share is five-sixth of a share and c share is four-fifth of b share

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Question 1039340: divide $1500between a,b and c such that b share is five-sixth of a share and c share is four-fifth of b share
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Write an equation for each phrase, get all three in terms of b
:
divide $1500 between a,b and c
a + b + c = 1500
:
such that b share is five-sixth of a share
b = 5%2F6a
multiply both sides by 6
6b = 5a
divide both sides by 5
a = 6%2F5b
:
and c share is four-fifth of b share
c = 4%2F5b
:
Now we substitute for a and c and have:
6%2F5b + b + 4%2F5b = 1500
multiply by 5, get rid of the denominators
6a + 5b + 4b = 5(1500)
15b = 7500
b = 7500/15
b = $500 is b's share
then
a = 6%2F5*500
a = $600 is a's
and
c = 4%2F5*500
c = $400 is c's
:
They add up to $1500