# Suzy is ten years older than Billy, and next year she will be twice as old as Billy. How old are they now?

Let the age of Suzy be S. It is given that she is 10 years older than Billy. Let Billy be B years old. So S = B+10

Next year Suzy will be S+1 years old and Billy will be B+1 years. Also, Suzy will be twice as old as Billy. Therefore S+1 = 2(B+1)

=> S+1 = 2B + 2

=> B+ 10 +1 = 2B +2

=> B+11 = 2B +2

=> B = 9.

So Billy is 9 years old and Suzy is 9 +10 = 19 years old.

There ages of Billy and Suzy now are 9 and 19 respectively.

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Let Suzy's age be S

Let Billy's age be B

==> given that Suzy's 10 years older that Billy:

==> S = B + 10 ..............(1)

Next year :

Suzy's age will be S + 1

Billy Will be B+1

But given that Suzy will be twice Billy's age:

==> S+1 = 2 ( B+1)

==> S + 1=  2B + 2

==> S = 2B + 1

But from (1) we know that S = 10 + B

==> 10 + B = 2B + 1

==> B = 9

==> S = 19

Then Billy's age= 9

And Suzy's age = 19

Approved by eNotes Editorial Team