Extra cred

Trick question, no ages are given in the problem.

procarbinefreak wrote: mary is 12 and john is 6

same thing I was thinking, how did you come about the answer?

Mary is twice the age of John. I was using the lowest numbers as possible when I started. John was two and Mary was one, but I changed Mary to 5 because she was three years older than john, and since John is half marys age that would make him 2 1/2. But 12 and 6 probably works.

Mary is twice as old as John. Thats it...

 

Ok I think I found how do to it mathematically:

j = John's current age
m = Mary's current age

We know john is half Mary's age
2*j = m
and that also means the difference in age is equal to John's current age
j = m-j

Now since "John is twice as old as he was when Mary was three years older than he is now" (most confusing thing evar)
So John is twice as old as john-young

j = 2(j-young)

And j-young is Mary's age at that point (j+3), minus the difference in age (j).

j-young = j+3-j = 3

plug it back in to j=2(j-young) to get:

j = 2(3)

So John's current age is 6, Mary is twice that, 12.

There's probably an easier way to state that, but the key lies in that the difference in age is John's age, and that never changes.

Now that that's solved, here's a riddle:

As everyone knows, in English, most singular nouns can be made plural by simply adding an 's' or sometimes an 'es' to the end of the word. So, in most cases, every letter of the singular form of the noun will also be found in the plural form. Like, "shoe" and "shoes," or "bum" and "bums." There will be exceptions, of course. For example, the word "matrix" is the plural of matrices. And "bacterium," and "bacteria." But, even in those cases, just about every letter from the singular noun also appears in the plural form. The other day, I was rereading one of my favorite books, 'The Lord of the Rings,' when an unusual word caught my eye. Of course, this book is full of all kinds of weird words from imaginary languages. But. this particular word is a bona fide English word-- and it's a plural noun. It's an old word and it's not used much nowadays, but you will find it in just about any English dictionary. The singular form of this word, however, is a very common English word. But, here's the interesting part. The word in question is a plural noun but it has no letters-- none-- in common with the singular form. Not one single letter. The question is what are these two words? Here's a hint: you might guess that both of the words are rather short, or at least one of them is. Because the longer the word is, the better the chances that you would duplicate a letter.

Edited by Jack Carver - 01 March 2007 at 9:52pm

I think it was where you took

jx2=j+3

John is only half of Mary's age right now.
Back then, when Mary was 3 years older than John's current age, she was actually 3 times his age.

As 2 kids get older, their ages become closer and closer together by percentage (multiplication), but always the same amount of years by subtraction.

Jack Carver wrote: I think it was where you took jx2=j+3 John is only half of Mary's age right now. Back then, when Mary was 3 years older than John's current age, she was actually 3 times his age. As 2 kids get older, their ages become closer and closer together by percentage (multiplication), but always the same amount of years by subtraction.

thanks for that. your right i went back and looked and i was wrong.

^^if your in at least algebra one, its not that hard. i just messed up setting the problem up.

There are no ages given, so there is no point of reference. Any answer found would just be a possible solution at some point in their life, and pure speculation.

Jack Carver wrote: Wrong.2 variables, 2 equations.1 and only 1 answer.

example:


This number is twice as much as it was when another number was the same, plus three. This number is half of the same number now, whats the number?

You've got nothing to work with....

choopie911 wrote: Jack Carver wrote: Wrong.2 variables, 2 equations.1 and only 1 answer. example: This number is twice as much as it was when another number was the same, plus three. This number is half of the same number now, whats the number? You've got nothing to work with....

You still have two variables.  number and another number.

This is alittle more than algebra. This is more like pre-calculus.