Question 611044
You can express these two situations algebraically:
A+10 = 2(B+10) "Ten years from now (A+10), A will be twice as old as B (will be ten years from now) 2(B+10)" and 
A-5 = 3(B-5) "Five years ago (A-5), A was three times as old as B (was five years ago), (3(B-5))" Solve this for A to get:
A = 3(B-5)+5 and simplify to get:
A = 3B-15+5 or
A = 3B-10 Now substitute into the first equation:
(3B-10)+10 = 2(B+10) Simplify and solve for B.
3B =2B+20
{{{highlight(B = 20)}}} and...
A = 3B-10
A = 3(20)-10
A = 60-10
{{{highlight(A = 50)}}}
Check:
A+10 = 2(B+10)
50+10 = 2(20+10)
60 = 2(30)
60 = 60 and...
A-5 = 3(B-5)
50-5 = 3(20-5)
45 = 3(15)
45 = 45