Question 1039340
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 = {{{5/6}}}a
multiply both sides by 6
6b = 5a
divide both sides by 5
a = {{{6/5}}}b
: 
 and c share is four-fifth of b share
c = {{{4/5}}}b
:
Now we substitute for a and c and have:
{{{6/5}}}b + b + {{{4/5}}}b = 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 = {{{6/5}}}*500
a = $600 is a's
and
c = {{{4/5}}}*500
c = $400 is c's
:
They add up to $1500