Mary, who is sixteen years old, is four times as old as her brother. How old will Mary be when she is twice as old as her brother?

Question

Mary, who is sixteen years old, is four times as old as her brother. How old will Mary be when she is twice as old as her brother?

Answer 1

Right now Mary is 16 and her brother is 16/4=4. So then in X years, she will be 16+X and her brother will be 4+X. So we need to find how many years when mary is twice as old. So

 

16+X=2(4+X)

16+X=8+2x

solving gives X=8

 

but we are not done yet. We still need Mary's age when this happens. So we add 8 to her current age of 16 to get 24. Checking that in 8 years her brother will be 4+8=12 and yes mary will be twice as old When she is 24. 

Answer 2

At the indicated ages, Mary is 16 and her brother is 4 (since she is 4 times older than he is).  Some number of years later (the same for both of them, of course), she will be twice as old as her brother.  We can represent this fact in equation form as:

 

16+n = 2(4+n), where n = number of years later.  With a little algebra, you can solve this equation for n.  Then Mary's age at that point will just be 16+n.

 

Hope this helps!