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Simple math word puzzle

M

MisterPresident

Golden Member
The sum of the ages of Mike and Ed is 44. Mike is twice as old as Ed was when Mike was half as old as ed will be when ed is three times as old as mike was when mike was three times as old as ed. How old are mike and ed?


 
i have to be honest: i may be able to figure it out, but its going to take more than 5 seconds, so i wont bother.
 
Obviously, the series is divergent, so we have to take the twelfth derivative of f(x).

Simple elementary math my friend.
 
Let's work this out backwards.

The last phrase "when Mike was 3 times as old as Ed" implies that at one time Mike and Ed were one of the following age pairs:

(M,E) = (3,1), (6,2), (9,3), (12,4), (15,5), (18,6), (21,7), (24,8), (27,9), (30,10), OR (33,11)

There are 11 possibilities then-- number them 1 through 11.

So when "Ed is three times as old as mike was when Mike was three times as old as Ed" means Ed at that time was one of the following ages (based on Mikes age above):

Either 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, or 99.

Continuing, when "Mike was half as old as Ed will be when Ed is three times as old..." means that Mike at that time must be one of the following ages:

Either -, 9, -, 18, - , 27, -, 36, -, 45, or -

Note that possibilites 1,3,5,7, 9, and 11 aren't valid anymore as that would make Mike a fractional age and we assume their ages are always whole numbers.


Now the ages of Ed at the same time Mike was those ages above are:

Either -, 5, -, 10, -, 15, -, 20, -, 25, -

We know the Mike is current twice the age that Ed was at that time, so Mike is now:

Either -, 10, -, 20,-, 30, -, 40, -, 50, -

And hence Ed is currently:
Either 3, 6, 9, 12,15, 18, 21, 24, 27,

Unfortunately, none of these age pairs add up to 44-- so there is no solution. That is, of course, if you assume their ages are always measured in whole numbers.

If their ages can be fractional, you can see the pattern that Mikes current age is 5x for some x, while Ed's current age is 3x for the same x.

Hence, their total age is 5x + 3x = 8x. Setting 8x = 44, we get x = 11/2 = 5.5.

Hence, Mike is currently 27.5 and Ed is currently 16.5 years old.






EDIT: Spelling.
 
Originally posted by: MathMan
Let's work this out backwards.

The last phrase "when Mike was 3 times as old as Ed" implies that at one time Mike and Ed were one of the following age pairs:

(M,E) = (3,1), (6,2), (9,3), (12,4), (15,5), (18,6), (21,7), (24,8), (27,9), (30,10), OR (33,11)

There are 11 possibilities then-- number them 1 through 11.

So when "Ed is three times as old as mike was when Mike was three times as old as Ed" means Ed at that time was one of the following ages (based on Mikes age above):

Either 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, or 99.

Continuing, when "Mike was half as old as Ed will be when Ed is three times as old..." means that Mike at that time must be one of the following ages:

Either -, 9, -, 18, - , 27, -, 36, -, 45, or -

Note that possibilites 1,3,5,7, 9, and 11 aren't valid anymore as that would make Mike a fractional age and we assume their ages are always whole numbers.


Now the ages of Ed at the same time Mike was those ages above are:

Either -, 5, -, 10, -, 15, -, 20, -, 25, -

We know the Mike is current twice the age that Ed was at that time, so Mike is now:

Either -, 10, -, 20,-, 30, -, 40, -, 50, -

And hence Ed is currently:
Either 3, 6, 9, 12,15, 18, 21, 24, 27,

Unfortunately, none of these age pairs add up to 44-- so there is no solution. That is, of course, if you assume their ages are always measured in whole numbers.

If their ages can be fractional, you can see the pattern that Mikes current age is 5x for some x, while Ed's current age is 3x for the same x.

Hence, their total age is 5x + 3x = 8x. Setting 8x = 44, we get x = 11/2 = 5.5.

Hence, Mike is currently 27.5 and Ed is currently 16.5 years old.






EDIT: Spelling.
Click to expand...

wow, just wow. i have no idea whether you are right though. after at least trying to understand it
 
Originally posted by: stan394
Originally posted by: MathMan
Let's work this out backwards.

The last phrase "when Mike was 3 times as old as Ed" implies that at one time Mike and Ed were one of the following age pairs:

(M,E) = (3,1), (6,2), (9,3), (12,4), (15,5), (18,6), (21,7), (24,8), (27,9), (30,10), OR (33,11)

There are 11 possibilities then-- number them 1 through 11.

So when "Ed is three times as old as mike was when Mike was three times as old as Ed" means Ed at that time was one of the following ages (based on Mikes age above):

Either 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, or 99.

Continuing, when "Mike was half as old as Ed will be when Ed is three times as old..." means that Mike at that time must be one of the following ages:

Either -, 9, -, 18, - , 27, -, 36, -, 45, or -

Note that possibilites 1,3,5,7, 9, and 11 aren't valid anymore as that would make Mike a fractional age and we assume their ages are always whole numbers.


Now the ages of Ed at the same time Mike was those ages above are:

Either -, 5, -, 10, -, 15, -, 20, -, 25, -

We know the Mike is current twice the age that Ed was at that time, so Mike is now:

Either -, 10, -, 20,-, 30, -, 40, -, 50, -

And hence Ed is currently:
Either 3, 6, 9, 12,15, 18, 21, 24, 27,

Unfortunately, none of these age pairs add up to 44-- so there is no solution. That is, of course, if you assume their ages are always measured in whole numbers.

If their ages can be fractional, you can see the pattern that Mikes current age is 5x for some x, while Ed's current age is 3x for the same x.

Hence, their total age is 5x + 3x = 8x. Setting 8x = 44, we get x = 11/2 = 5.5.

Hence, Mike is currently 27.5 and Ed is currently 16.5 years old.






EDIT: Spelling.
Click to expand...

wow, just wow. i have no idea whether you are right though. after at least trying to understand it
Click to expand...

I didn't read the response but I looked at his username and thought "this man must know what he's talking about"
 
This is very simple to break down. Whatever Mike's age was when he was 3 times Ed's age, is what Ed's current age is. Therfore if Mike was 6 and Ed was 2, Ed's current age is 6 and Mike's is 10. If Mike was 12 and Ed was 4, Ed's current age is 12 and Mike's is 20. If Mike was 18 and Ed was 6, Ed's current age is 18 and Mike's is 30. You can narrow in very quick and see Mike is 27.5 and Ed is 16.5



When Mike was 16.5 Ed was 5.5, therefore Ed would be 49.5 (3 times mikes age when mike was 3 times older than ed), Mike would be 24.75 (half of 49.5) and ed would be 13.75 (because Mike is 11 years older-16.5 minus 5.5). We then double Ed being 13.75 to get Mike an age of 27.5. Since Ed is 11 years younger, Ed is 16.5. 16.5+27.5=44.
 
Originally posted by: MathMan
Let's work this out backwards.

~~~~~~~~~~~~~~~
bunch of stuff i don't understand
~~~~~~~~~~~~~~~

Hence, Mike is currently 27.5 and Ed is currently 16.5 years old.


EDIT: Spelling.
Click to expand...

people like you show the world just how stupid people like me are.

 
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