Need help with my math

[zamorush]

If anyone feel really really bored, or really smart, could you guys help me solve this problem?

My Calc teacher teacher gave me this take home quiz with a totally weird problem not in any way related to calculus.

Consider the conversation:

George: I know three people and the product of their ages is 2450 while the sum of their ages is twice yours. How old is the oldest?
Frank: I don't know.
George: Of Course not, but the oldest is younger then me.
Frank: Ah, now i know how old is the oldest one is.

Question: What are the ages of trhee people?


There is a trick here. And you can get a numerical answer, but using any variables won't do the trick. There is some clue in the conversation. With all my powerful knowledge in math going through all the calc clases, i can't solve this one. Feel kind of dumb.

nik

[mohrds]

Here's my stab

f=Frank
g=George
u=unknown person

f*g*u=2450 and 2f=g+u
.5(g+u)*g*u=2450

The rest should be a nice Calculus problem you can handle.

Doug

[zamorush]

Here's my stab

f=Frank
g=George
u=unknown person

f*g*u=2450 and 2f=g+u
.5(g+u)*g*u=2450

The rest should be a nice Calculus problem you can handle.

Thanks Doug, but see, I've tried that already, that is one way how you won't solve the problem. It does not come up to the whole number. Comes up with imaginary numbers.

Apparently there is a clue in the conversation, however I with my limited knowledge of english can't catch the hint or clue. Also, my teach said that he gave the problem to his Algebra 1 students, and they solved it. So it not suppose to be that hard.

nik

It seems to me, based on the set up that there are more variables here. It doesn't say that George knows ONLY three people. So it could be anybody that equals 2450.

Variables:
a,b,c (with c being the oldest) = people known
g = George
f = Frank

a*b*c = 2450
a+b+c = 2f
c < g

Do we not know the ages of George and Frank?

WORKING BACKWARDS:
If you take 2450 and break it down into its factors, you get: 2, 5, 5, 7, 7.

That means the ages have to be one of the following combinations:

2, 25, 49
5, 10, 49
5, 14, 35
7, 10, 35
7, 14, 25
(2,35,35 won't work because "c" is the oldest so you'd need an oldest).

Maybe, by knowing the possible answers, you can work backwards. Hope this helps.

[mohrds]

Originally posted by zamorush


Thanks Doug, but see, I've tried that already, that is one way how you won't solve the problem. It does not come up to the whole number. Comes up with imaginary numbers.

Apparently there is a clue in the conversation, however I with my limited knowledge of english can't catch the hint or clue. Also, my teach said that he gave the problem to his Algebra 1 students, and they solved it. So it not suppose to be that hard.

nik

Oh I get it.

George is the oldest, Frank is the middle age and the unknown is the youngest.

Frank is as close to George as the unknown is, in fact, george is equadistant between the youngest and the oldest.

Hmmm, This is going to bug me. I'll pen it out for a bit.

Doug

I GOT IT! I GOT IT!

As I said, the factors of 2450 are: 2x5x5x7x7. So that means the people could be only one of these sets of ages:
2,5,5x7x7 = 2,5,245 sum = 252
2,7,5x5x7 = 2,7,175 sum = 184
2,5x5,7x7 = 2,25,49 sum = 76
2,5x7,5x7 = 2,35,35 sum = 72
2x5,5x7,7 = 10,35,7 sum = 52
2x5,5,7x7 = 10,5,49 sum = 64
2x7,5,5x7 = 14,5,35 sum = 54
2x7,5x5,7 = 14,25,7 sum = 46
2x5x7,5,7 = 70,5,7 sum = 82
2x7x7,5,5 = 98,5,5 sum = 108
2x5x5,7,7 = 50,7,7 sum = 64

Frank knows that the sum is twice his age. Of course he knows his own age so if only one set of ages was twice his age, he could have figured it out. But there had to have been more than one answer for him to require more information so the sum had to equal 64 (the only two where the sum equalled the same thing).

2x5,5,7x7 = 5,10,49 sum=64
2x5x5,7,7 = 50,7,7 sum=64

George's clue that he is older than all three people is what is neccessary to figure out which answer it is. If George was 75 (or an age over 50), it wouldn't help Frank narrow down the answer. If George is say 35 (or an age less than 49), it cuts both answers out. BUT if George is 50, then it can't be 50,7,7 because George is OLDER than the oldest. So it must be 5,10,49 for the answer.

So the three people are 5,10, and 49
Frank is 32
George is 50

Tada!!!!

[zamorush]

That means the ages have to be one of the following combinations:

2, 25, 49
5, 10, 49
5, 14, 35
7, 10, 35
7, 14, 25
(2,35,35 won't work because "c" is the oldest so you'd need an oldest).

Maybe, by knowing the possible answers, you can work backwards. Hope this helps.

It does help,

I guess that is how you suppose to do it. Those are all could be the right answers, however when you add them together to get the sum of ages:

2 + 25 + 49 = 76
5 + 10 + 49 = 64
5 + 14 + 35 = 54
7 + 10 + 35 = 52
7 + 14 + 25 = 46

And consider that George and Frank to be part of the group, then one of them has to has his age equal to the half of the sum of all ages. That does not happen though.

So Frank is the oldest after George, and that is whom George is talking about, right? Then Frank has to be the middle column. Unfortunatelly he can be as old as 50, but still that won't add up to 76.

I'll keep thinking.

nik

[zamorush]

WOW, very interesting. I need to get the logic down here.


I see now...... so both George and Frank were not part of the group. They were just their for confusion, he he. And all it was for that problem was simple factroing the number.

Well, thanks a lot John, that was very nice of you spending your time helping me out here.

Although now i feel kind of dumb, not getting the logic right, he he.

thanks again

nik

[zamorush]

Well, after I did just a little bit more thinking, I came up with an alternative solution to the problem.

One of the factors that we haven't considered is:

1x49x50, which adds up to 1+50+49 = 100

When George says that he knows 3 people, he also consideres Frank as one of them. If that is the case, then Frank is 50 years old, and his age is 2*50 = 1+50+49, what is stated at the begining.

If you solve this problem the other way around, which is factoring, and looking for the same answer, then I think that you can emmit the part where George says, "and the sum of their ages is twice yours," because then even if we did not know about how old Frank reallly is or what the sum of their ages add up to, we could still factor 2450 out, and find the ages of three people. I think this solution might not be the correct one, because then why would they include the fact that Frank is twice the sum?

what do you guys think?

nik

If Frank is 50, then 1, 49, and 50 does work. However, if that's the case, Frank does not need to ask George for more information. Why? Because there is only one set of ages that adds up to 100.

The fact that Frank needs more information to determine the answer must mean there is more than one solution to choose from. When George tells him "the oldest is younger then me" it gives Frank the information necessary to narrow the solutions down to only one.

I'm sticking with:

The three people are 5,10, and 49
Frank is 32
George is 50