Intermath | Workshop Support

 Write-up

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?

Problem setup

I will need to set up an equation where one side shows a number (n) added to 129 on one side, and 2 times 129 – the number (n).  When I solve the equation, I should come up with a number to solve both sides of the equation.

Plans to Solve/Investigate the Problem

In class, we set up an equation to solve the problem.  We also used Excel to help us discover the answer.  If we did it successfully, we should be able to find one number that will satisfy the equation.

Investigation/Exploration of the Problem

The first thing I did was to use Excel to compare numbers.  Below is the Excel sheet I used.

 N N + 129 129 - N 2(129-N) 50 179 79 158 51 180 78 156 52 181 77 154 49 178 80 160 47 176 82 164 45 174 84 168 43 172 86 172

I tried 50 as “n”, then tried the next 2 higher numbers, to try to get the two yellow columns equal.  When the difference between those numbers was getting higher by raising the value of “n”, I tried lowering the value of “n”.  The two columns started getting closer in numbers.  I finally found 43 as the answer; If n = 43, then 43 + 129 = 2 (129 – 43).  172 = 86 * 2 or 172.

Next we tried writing an equation.  This was easy to do, because I’d already done most of the work using Excel.  N + 129 = 2 ( 129 – N)

N + 129 = 258 – 2N

3N = 129

N = 43

Author & Contact
Meg Ramsey
mramsey@rockdale.k12.ga.us

Link(s) to resources, references, lesson plans, and/or other materials
Solving an Equation