Question 16484
Good question. It requires you to change the information into a system of equations. First of all we know that the "joint ages of A and B is 82 years", which gives us: A + B = 82. Secondly we know that "in 6 years time A will be twice as old as B was 4 years ago" giving us: A+6=2(B-4). 
<br>
Now that we've got the equations, we can manipulate the second one (A+6=2(B-4)) so that it reads: A=2(B-4)-6 (because we want A on its own, so that we can substitute it into the first equation). Simplify the equation and you get: A=2B-14. Now that we've got this, we can substitute it into A+B=82 (for A), so that it reads: (2B-14)+B=82.
<br>
Now we simplify this by foiling everything, which gives us: 3B-14=82. Next, we add 14 to both sides to get: 3B=96. Then we divide both sides by 3, to leave us with:
<br>
B=32
<br>
Now that we know that, we can plug that value of B into the first equation to determine A: A + 32 = 82. And so we add (-32) to both sides, which leaves us with:
<br>
A=50
<br>
And there it is. Solved.