John's Losing His Marbles

Date: 8/26/96 at 11:29:16
From: Raymond
Subject: Losing Marbles

Dear Dr. Math,

Kindly advise the following :

John has twice as many green marbles as red marbles. When John lost 42 
green marbles, he had half as many green marbles as red marbles. How 
many marbles had he altogether at first?

I look forward to hearing from you soon. 

Thanks and best regards.

Date: 8/26/96 at 15:20:59
From: Doctor Robert
Subject: Re: Losing Marbles

Let x be the number of red marbles that John originally had.  Then, 
according to the problem, the original number of green marbles is 2x.  
Now when John lost 42 green marbles, he must have had 2x-42 green 
marbles.  According to the problem, this number is one half of the 
number of red marbles.  We can write the equation

     2x-42 = (1/2)x
   4x - 84 = x
        3x = 84
         x = 28.

So, he orginally had 28 red marbles and 56 green marbles for a total 
of 94 marbles.  Unfortunately, John is losing his marbles.

You can check to see whether the answer is correct.  If John loses 42 
green marbles he then has only 14 green marbles which is (1/2) of 28, 
the number of red marbles.  So, we know we're right.  That's what I 
like about word problems!

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/