Ms. Krump's Age

Date: 10/05/1999 at 00:29:43
From: Amanda
Subject: Ms. Krump's age

One day in math class Shelly asked, "Ms. Krump, how old are you?"

Ms. Krump calmly replied, "This year I'm 3 times as old as my little 
sister. However, 6 years ago I was 5 times as old as she was."

"Well, that doesn't help," yelled Clara.

"Sure it does" said Frank.

"I don't get it," complained Brian.

Ms. Krump said, "Think about it some more and we will see how many of 
you can guess my age when we have class tomorrow."

How old is Ms. Krump?

I haven't really tried anything yet because I don't really understand 
it. If you could get the answer (or the method, if there is one) to 
me, I would greatly appreciate it. Thanks for your help.

Amanda

Date: 10/05/1999 at 11:24:48
From: Doctor Rob
Subject: Re: Ms. Krump's age

Thanks for writing to Ask Dr. Math, Amanda.

Pick one of the ages and assign a name to it. Say you pick the younger 
sister's current age, and call it S (for sister). Then Ms. Krump's age 
now is 3*S, according to her first statement.

Now go back six years. Each person's age is smaller by 6. Ms. Krump's 
age then was 3*S - 6, and her sister's age then was S - 6. Now you can 
use Ms. Krump's second statement to set up an equation involving S. 
This you solve for S, and then 3*S is the answer you seek, Ms. Krump's 
current age.

Suppose you instead pick Ms. Krump's current age, and call it K (for 
Krump). Then her sister's current age is K/3, according to the first 
statement. Six years ago their ages were K - 6 and K/3 - 6. Now using 
the second statement, you can set up an equation involving K. Solving 
this for K will give you the answer sought.

For more about age-type word problems, see the following web page from 
our Classic Problems collection:

   Age Word Problems 
   http://mathforum.org/dr.math/faq/faq.age.problems.html   

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

Date: 10/05/1999 at 23:22:32
From: Scott Griffin
Subject: Re: Ms. Krump's age

Thanks a lot for the formula - it really helped! In fact, I even got 
the answer. Ms. Krump is now thirty years old, and 6 years ago she was 
24.

       10 * 3 =   30
     -  6       -  6
       --         --
        4         24
     *  6
       --
       24

Sincerely,
Amanda

Date: 10/06/1999 at 09:01:35
From: Doctor Rob
Subject: Re: Ms. Krump's age

Sorry, Amanda, but that's incorrect. Six years ago she was only *FIVE* 
times as old as her sister, not *SIX* as you seem to have used.

Try again!

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

Date: 10/06/1999 at 10:44:32
From: Scott Griffin
Subject: Re: Ms. Krump's age

Thank you for telling me that. I guess that I was so happy that I knew 
how to figure it out, that I didn't even read the paper and went off 
doing a different thing.

However, this time I think that I' ve really got the answer.

       12 * 3 =   36
     -  6       -  6
       --         --
        6         30
     *  5
       --
       30

Ms. Krump is now 36, and 6 years ago she was 30. Ms. Krump's younger 
sister is now 12, and 6 years ago she was 6.

Date: 10/06/1999 at 11:04:42
From: Doctor Rob
Subject: Re: Ms. Krump's age

You've got it now - good work! Now do some different ones of the same 
kind, and you'll show yourself that you understand how to do many 
problems like that.

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