Sum Twice the Difference

Date: 10/18/2002 at 06:41:15
From: Jamie
Subject: Math 

What number can you add to and subtract from 129 such that the sum 
is twice the difference?

Date: 10/18/2002 at 12:36:21
From: Doctor Peterson
Subject: Re: Math 

Hi, Jamie.

We could do this using algebra, if you know any; but let's just think 
about what's happening, and look for an easy way to solve it.

Suppose we compare the sum and difference of any two numbers; I'll add 
5 to and subtract 5 from 12:

    12 + 5 = 17
    12 - 5 = 7

You can see that the two numbers we get differ by 10. Can you see 
where the 10 comes from?

    0                    7             12             17
    +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+-->
                         |<-------------|------------->|
                                 5              5

Now, in order for one to be twice the other, the difference (10 in 
this case) would have to be equal to the smaller of the two numbers 
(the 7 here).

So we want to find a number "x" to add and subtract so that it looks 
like this:

    0                         dif           129           sum
    +----------------------------------------+----------------->
                               |<------------|------------>|
                                      x             x
     \________________________/ \_________________________/

with the two big marked distances the same. Can you see a way to 
figure out how to do this?

If you have any further questions, feel free to write back.

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