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Jack is Older than Jill

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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
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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/
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Associated Topics:
High School Basic Algebra
High School Puzzles
Middle School Algebra
Middle School Puzzles

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