Question 662667
I think the original solver got this one wrong.  
Let's let i = Ivan's age and m = Mary's age.  Ivan is 3 years older than Mary, so 
{{{i = m + 3}}}
The next one is a little tricky.  One third of Ivan's age is two years less than one half of his sister's age one year ago.  So
{{{i/3 = (m-1)/2 - 2}}}
To simplify the rest of the solution, let's multiply both sides of the above equation by 6:
{{{6*(i/3) = (6*(m-1))/2 - 6*2}}}
{{{2*i = (6*m - 6)/2 -12}}}
{{{2*i = 3*m - 3 - 12}}}
{{{2*i = 3*m - 15}}}
Substituting m+3 for i (from the first equation) gives us
{{{2*(m+3) = 3*m - 15}}}
{{{2*m + 6 = 3*m - 15}}}
Subtract 2*m from both sides:
{{{2*m + 6 - 2*m = 3*m - 15 - 2*m}}}
{{{6 = m - 15}}}
Add 15 to both sides:
{{{6 + 15 = m - 15 + 15}}}
{{{21 = m}}}
So Mary is 21 and Ivan is 24.

We can check our answer by inserting our values for i and m into the original second equation:
{{{24/3 = (21 - 1)/2 - 2}}}
{{{8 = 20/2 - 2}}}
{{{8 = 10 - 2}}}
{{{8 = 8}}}
So our calculations are correct.