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Title
Double Trouble

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

(Source: Mathematics Teaching in the Middle School, Jan-Mar1995).


Problem setup

 

There is a number that added to 129 can also be subtracted from 129, and is equal to two times the difference between 129 and the original number.  What is that number?

 

Plans to Solve/Investigate the Problem

In trying to discover the answer, I needed a variable (x) to take the place of it so I could develop a problem.  The problem reveals itself to be an equality problem by using the words “such that”.  Once I had the equation, then I could solve for “x”.

 

Investigation/Exploration of the Problem

 

“What number can you add to 129” -- This part was easy.  X + 129.  The next part seemed tricky --“and subtracted from 129” -- I began to look for an importance of this phrase.  I discovered that the importance of this answer is in the second half of the equality.  I didn’t need to have this figured into the left side of the equality.  However, this phrase caused me to look for a number that was smaller than 129.  “Such that the sum of the number and 129” – this reiterates the first side of the equality.  “Is twice the difference between 129 and the number?” –- This is 2 times 129 minus x or 2(129 – x). 

So the final equality looks like this: 

                                                   x + 129 = 2(129 – x) 

 

When I multiplied 2 times 129 I got 258 and 2 times x is ‘2x’.  After getting my variables all on one side, my equation looked like this:

 

                                                    3x + 129 = 258

 

I then subtracted 129 from both sides and came up with 3x = 129.  Then I divided both sides by 3 in order to have only ‘x’ on one side and my answer was x = 43.   

Extensions of the Problem

In the midst of doing the problem, I discussed with others whether or not the answer needed to be a positive number.  Much time was spent discussing the phrase “the difference between 129 and the number” and whether or not it implied that the answer was less than 129 or if it could be vice versa. 

 

Author & Contact
Kevin Smith

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