A Problem to solve

Subject: A Problem to solve Tue Feb 24, 2009 10:51 pm

I've been preparing for an exam lately (not the best of times), and this math problem have been killing me for the past two days! I'm just posing it here hoping that someone could give it a try. Your help will be greatly appreciated.

Two teenagers, a boy and a girl, are out on their first date. After seeing a movie, they end up at a hamburger restaurant. Both are rather shy, and don't know what to talk about. Eventually, the boy breaks the silence, and the ensuing conversation goes like this:

He: “Do you have any brothers?”
She: “Yes, three.”
He: “What are their ages?”
She: "I hear that you are good at arithmetic. So, I'll give you that information in the form of a puzzle: Their ages (all whole numbers), when multiplied together, are equal to the age of my grandmother, who is seventy-two.”

The boy does some calculations on a paper napkin.

He: “That doesn't give me enough information.”
She: “Their ages, when added together, are equal to the number of tables in this restaurant.”

The boy does some more calculations on the napkin, and then looks around.

He: “I’ve counted the tables, but still can't tell their ages!”
She: “I'll give you one last clue: The name of my youngest brother is Jimmy.”
He says: “Aha!”, and gives her the correct ages other brothers.

What are the ages of the girl’s brothers?

Guest

12, 3 and 2?

12*3=36

36*2=72

o.O

Which also would equal 17 tables in the restaurant..

Subject: Re: A Problem to solve Tue Feb 24, 2009 11:06 pm

you have several unknowns in this problem.

x y and z the ages of the 3 brothers.

and a the number of tables.

you know that

x x y x z = 72

x + y + z = a

72 = 2 x 4 x 9
and
72 = 3 x 3 x 8

Sibce there is a younger brother, then I guess it's the first solution : 72 = 2 x 4 x 9

So Jimmy is 2 years old and the others are 4 and 8 and there are 14 tables in the restaurant.

Edit : Kaylee's number could also work.

I depends on the number of tables in the restaurant.

Edit 2 : yet an other possibility is 2 6 and 6 since 2*6*6=72

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Guest

mm. That's why I disliked math in high school. They would give you problems that you weren't supposed to figure out, but just notice 'not enough information' or something. I hate math.

Subject: Re: A Problem to solve Tue Feb 24, 2009 11:15 pm

I loved Maths, I had good grades and it was challenging, but I'm glad it's over

this problem is quite hard, but once you know how it works it's very easy. Real problems are : how many tables in the restaurant ?
Does she have twins brothers ?

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Subject: Re: A Problem to solve Wed Feb 25, 2009 7:20 am

Thanks for the help. Kaylee, I got your answers too but there were other possibilities such as:

2*4*9=72
4*6*8=72
12*3*2=72
8*3*3=72
18*2*2=72
2*6*6=72

The fact that the girl in the problem revealed that 'Jimmy' was her youngest brother seemed like a clue that there were no twins (at least that what it seemed like to me). Therefore, I thought that the last three statements (8*3*3=72, 18*2*2=72 and 2*6*6=72) were wrong.

I agree with Dax that the real problem is in the number of tables in the restaurant. Also, thanks for translating the problem into algebraic terms Dax. I forgot about that. It certainly makes the problem easier to handle.