Jack is Older than Jill

Date: 11/16/2001 at 18:39:02
From: Danielle
Subject: Jack and Jill

Here is the problem:

Jack is married to Jill. Their son, Junior, asks each of them to tell 
him their ages. Junior's parents decide to tell him, but in the form 
of a puzzle. Jack says to Junior, "if you reverse the digits in my 
age, you get your mother's age." Jill tells her son, "The sum of my 
age and your dad's age is equal to 11 times the difference in our 
ages."

"Wait a minute," says Junior, "I can't figure out your ages with just 
those two clues!"

"You're right," said Jack, "Remember that I am older than your 
mother." 

What are the ages of Jack and Jill?

Danielle

Date: 11/17/2001 at 02:04:44
From: Doctor Jeremiah
Subject: Re: Jack and Jill

Hi Danielle,

Remember that a number can be split into its place values; for example 
45 = 4 * 10 + 5 and 27 = 2 * 10 + 7 (we'll use * to mean multiply).

   So let Jack's age be  a * 10 + b

Then "if you reverse the digits in my age, you get your mother's age."

   So let Jill's age be  b * 10 + a

And "The sum of my age and your dad's age is equal to 11 times the 
difference in our ages."

So the difference in the ages must be positive, because the sum will 
be positive. So the difference must be "Jack's age - Jill's age" and 
the equation for that sentence will be:

    Jack's age  +  Jill's age  = 11 * ( Jack's age  +  Jill's age )
   (a x 10 + b) + (b x 10 + a) = 11 * ((a x 10 + b) - (b x 10 + a))

Simplify that and get something that equates b and a. Then figure out 
the smallest values of b and a that will work in the answer. Then when 
you have workable answers for b and a, calculate Jill's age and Jack's 
age.

Let me know if you get stuck.

- Doctor Jeremiah, The Math Forum
  http://mathforum.org/dr.math/