Stickers

Date: 8/22/96 at 9:17:24
From: Anonymous
Subject: Stickers

Jack and Paul together have 270 stickers.  Jack will have twice as 
many stickers as Paul if Paul gives him 18 stickers.
a) Find the number of stickers Paul starts with.
b) How many more stickers does Jack have than Paul at the beginning?

Date: 8/30/96 at 14:38:32
From: Doctor Jerry
Subject: Re: Stickers

Let J be the number of stickers Jack has at the beginning and P be the 
number of stickers Paul has at the beginning.  The first sentence says 
that 
  
   J + P = 270.

The second sentence is trickier and you should read it very, very 
carefully.  After Paul gives Jack 18 stickers, Paul will have P-18 
stickers and Jack will have J + 18.  We are told that 

   J + 18 =2 (P - 18).

So, we have the two equations

   J + P = 270
   J + 18 = 2P - 36.

If you subtract these equations, the J will go away.  The result is

   P - 18 = 270 - (2P - 36) = 270 - 2P + 36.

Take the -2P to the left and the -18 to the right.  This gives

   3P = 270 + 36 + 18
   3P = 324
    P = 108.

Since J + P = 270, J = 270 - 108 = 162.

So, the answer to 
a) is 108 and the answer to 
b) is J - P = 162 - 108 = 54.

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