What Are Their Ages?


Of three sisters named April, May, and June, none is yet twenty-one. 
April is now as old as June was fourteen years ago, and two-thirds of May's age. 
May, on the other hand, will be June's age when May is twice as old as she is 
now plus two years. Three years ago, May was as old as April is now.
How old are April, May, and June? 
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Answer:
April is 6, May is 9 and June is 20

Solution:
Let's let A=April, M=MAy, and J=June
Now from statement 1, we know that: "April is now as old as June 
was fourteen years ago, and two-thirds of May's age."   Expressed mathematically:
 A = J - 14  and A = 2/3M

From statement 2, "May, on the other hand, will be June's age when May is 
twice as  old as she is now plus two years."  Expressed mathematically:
M x 2 + 2 = J

And from statement 3, "Three years ago, May was as old as April is now."
Expressed mathematically:  M - 3 = A

Substituting for A in the 2nd expression from statement 1, we get M - 3 = 2/3M
which reduces to  M - 2/3 M = 3  or 1/3M = 3, or M = 9 so May is 9.

Substitute in the expression from statement 3 and we get 9 - 3 = A or A = 6, so April is 6.

Substitute in expression 1 and we get 6 = J - 14 or J = 20 so June is 20.