Jack is Older than JillDate: 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/ |
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