Mindbender

[AndrewD]

This was in my son's 7-11 IQ work out book. I still can't figure out the methodology to get the answer, even after looking up the answer!

Jack and Martha have been married for 20 years. If you add Jacks age to Martha's you get a combined age of 91 years. Jack is now twice as old as Martha was when he was as old as she is now. From this information, can you work out how old Jack and Martha are now?

Anyone care to explain to me (preferably in a way I can explain to a 9 year old too)?

Thanks!

A

Um. no.

That middle sentence makes no sense to me!

clearly you are supposed to put it into algebraic equations

so where Jack = J and Martha =M

J+M=91

but the next sentence implies we are talking about 20 years ago, ie at a time when J+M=71.

Then I get lost. sorry.

What was the answer given?!

OK Here goes:

Call Jack J and Martha M

J+M=91

It is asking about a time when J was the same age as M is now. This was J-M years ago.

At that time J's age now is double what M's age was then. So M's age then was M-(J-M)
So J=2(M-(J-M))
=2(M-J+M)
=4M-2J
SO 3J=4M
Going back to J+M=91 and multiplying by 3
3J+3M=273
Substituting for J,
4M+3M=273
7M=273
M=39
So J=52
The 20 years is a red herring. It was actually 13 years ago when Jack was the same age as Martha is now.

Good luck explaining this to a 9 year old !!!

Wow, so presumably they would have dated for a couple of years before tying the knot - what the hell was a 30 year old man doing with a 17 year old girl?!! What message is this sending to our children?

Richmal, I think the appropriate 9 year old response here is

"you legend"

Wow.

Thanks!