Question 1005246
 One number is 5 bigger than another number.
 When one third of the smaller number is added to half the bigger number the answer is 10.
 Find the smaller number
:
Two numbers, a & b, b is the smaller
:
a = b + 5
and
{{{1/3}}}b + {{{1/2}}}a = 10
multiply equation by the least common multiple of the denominators, 6
6*{{{1/3}}}b + 6*{{{1/2}}}a = 6(10)
Cancel the denominators 
2b + 3a = 60
We know a = b+5
2b + 3(b+5) = 60
2b + 3b + 15 = 60
5b = 60 - 15
5b = 45
b = 45/5
b = 9 is the smaller number
:
:
a = 9 + 5 = 14
Confirm this in the statement,"When one third of the smaller number is added to half the bigger number the answer is 10."
{{{1/3}}}*9 + {{{1/2}}}*14 = 10
 3 + 7 = 10