How Old is Chris Now?

Date: 12/26/2001 at 13:45:49
From: Fatama Akther
Subject: Word problems

Here is my question:

Pat and Chris have the same birthday. Pat is twice as old as Chris was 
when Pat was as old as Chris is now. If Pat is 24 now, how old is 
Chris now?

I have tried doing many things. First I tried to solve by just reading 
it, but it's confusing. Can you please help me?

Thank you.

Date: 12/27/2001 at 12:36:27
From: Doctor Jody
Subject: Re: Word problems

Hi Fatama,

It does seem to be a confusing problem while reading it. I'm going to 
write things down to see if I can make it clearer.

What do I know? I know that Pat is 24 years old now. And I know that 
Pat is older than Chris for two reasons: 

1. "Pat is twice as old as Chris was" - oh wait! They're talking about 
Chris's age at some time in the past, so Pat could be either older or 
younger than Chris. For example, if it's talking about when Chris was 
2, say 10 years ago, and Pat is 4 now, then Pat could be younger than 
Chris. Or, if Chris was 2 last year and Pat is 4 now, then Pat's 
older.

2. "when Pat was as old as Chris is now" - this certainly makes Pat 
older than Chris, even though the first reason is no longer as clear.  

That's not helping me a lot, other than telling me that Pat's not 
currently younger than Chris. Which is okay.

Now, if Pat is 24, then Chris was 12 (half Pat's current age) at some 
point in the past. That point was when Pat was as old as Chris is now.  

Restating it, some number of years ago - let's call it x - Chris was 
12 and Pat was Chris's current age.  

Finding how long ago that was will help us find how old Chris is now.

I'm going to write down in equation form everything I know, and see 
what I can pull out of it.

 1. Pat_now    = 24

 2. 24         = 2 * Chris_then

 3. Chris_then = 12

 4. Chris_now  = 12 + x        x years later, Chris is 12 + x

 5. Pat_then   = Chris_now     Pat's age then is Chris's age now

 6. Pat_then   = Pat_now - x   also, Pat was x years younger back then

 7. Pat_then   = 24 - x        using Pat's current age for Pat_now

 8. 24 - x     = Chris_now     using Pat_then's age (24-x) for the
                               amount on line 5

 9. Chris_now  = 24 - x        switching the sides of line 8

10. Chris_now  = 12 + x        just copying down line 4

11. 24 - x     = 12 + x        substituting Chris-now in line 10 for 
                               the value in line 9

See if you can take it from there. The value you come up with for x 
should be the number of years ago that the problem is talking about.  
Then you'll need to plug it in to check it and to get Chris's current 
age.  

I hope this helps. Please write back if you have more questions about 
this or about something else.

- Doctor Jody, The Math Forum
  http://mathforum.org/dr.math/   

Date: 12/29/2001 at 14:59:22
From: Fatama Akther
Subject: Word problems

Dr. Math,

I think I found the answer: Chris is 18 now.

First I solved for x and got 6. I then plugged 6 into 24-x, which gave 
me 18.

Thank you.