Friday, July 11, 2008

How old is Mark?

For everyone that struggled with the pencil puzzle, here's another algebra puzzle to "stretch your neurons". Pay attention...

The combined ages of Mark and Ann are forty-four years, and Mark is twice as old as Ann was when Mark was half as old as Ann will be when Ann is three times as old as Mark was when Mark was three times as old as Ann.

How old is Mark?

7 comments:

1. Just figured it out...
ARE YOU KIDDING ME?

Not sure how to NOT spoil it.
I see why you mentioned the pencil puzzle.

2. I can tell you have the right answer... :-)

3. to help others make some sense of the confusion...

start with the last part, "when Mark was three times as old as Ann". Let's say x = Ann's age in years at that point. Then Mark would be 3x. Also note that the difference is always 2x. And that Ann is younger than Mark.

Now work your way back up.
"when Ann is three times as old as Mark was..." = 3(3x)
"when Mark was half as old as Ann ..." = 3(3x)/2

"as Ann was when Mark was..."
remember the difference in age is 2x, so Ann's age is the above minus 2x: 3(3x)/2 - 2x

and finally, "Mark is twice as old as Ann..." = 2 ( 3(3x)/2 - 2x )

Okay, that is Mark's current age relative to Ann's age at the end of the huge sentence. Most of the work is done now for you.

What's Mark's age?

4. Much reminds me also of the Steamboat Boiler Age Puzzler. Not so hard to do but the language of then, now and later gets all confused in our all too small brains, no matter how smart we are.

5. Great E-Mail from my Friend Ron.

Jen's cat is one third the age that Ron was when Ron was two times the age that Greg will be when Ron received Greg's e-mail math problem that drove Ron to insanity. :<)

6. From the above equation, Mark is currently 5x years old where x is Ann's age when Mark was three times her age.

Ann is 2x years younger, thus she is 3x years old.

The combined age is 44, so
5x + 3x = 44
8x = 44
x = 5.5

Thus Mark is currently 27.5 years old and Ann is 16.5 years old.

Yeah, that's right. Blaine couldn't have made their combined sum equal 88 or some other nice multiple of 8. He had to get into fractions. Thanks Blaine! ;)

7. At least I didn't go into a fraction smaller than 1/2... I was being nice. :-)

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