Question 1129133
three girls share a packet of sweet. the first received 2/5 of the sweets.
 the second received 5/9 of the remainder and the third got 8 sweets.
how many sweet were in the packet? 
:
let a = total amt of sweets
change 2/5 to .4, simplify dealing with fractions
a = .4a + {{{5/9}}}(a-.4a) + 8
a = .4a + {{{5/9}}}(.6a) + 8
multiply equation by 9 to get rid of the denominator
9a = 9(.4a) + 5(.6a) + 9(8)
9a = 3.6a + 3a  + 72
9a = 6.6a + 72
9a - 6.6a = 72
2.4a = 72
a = 72/2.4
a = 30 sweets in the packet
:
:
See if that checks out
{{{2/5}}} * 30 = 12 for the 1st girl
{{{5/9}}} * 18 = 10 for the 2nd girl (subtracted 12 from the total)
3rd girl: 8
----------------
total 30