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Linear Algebra

Hello all!

I humbly apologise in advance if I'm posting inappropriately, or asking for a solution that is technically beneath you.

Problem is as follows:

"When Mary was half as old as Sam was when Mary was as old as Sam was when Mary was as half as old as Sam is now, Sam was four times as old as Mary was when Sam was a third as old as he is now.
Ages are in complete years, so how old must Mary be?"

Thank you in advance of any assistance!

Solution Preview

Please see the attached file.

Problem

When Mary was half as old as Sam was when Mary was as old as Sam was when Mary was as half as old as Sam is now, Sam was four times as old as Mary was when Sam was a third as old as he is now.

Ages are in complete years, so how old must Mary be?

Solution

This is certainly very confusing on first inspection; however it can be conquered by going through each phrase slowly.

Let's rewrite the question:

When Mary was
half as old as Sam was
when Mary was as old as Sam was
when Mary was as half as old as Sam is now,
Sam was four times as old as Mary was
when Sam was a third as old ...

Solution Summary

This solution is comprised of a detailed explanation to answer when Mary was half as old as Sam was when Mary was as old as Sam was when Mary was as half as old as Sam is now, Sam was four times as old as Mary was when Sam was a third as old as he is now, so how old must Mary be?"

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