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 Write-up

Title
Mystery Number

Problem Statement
What is the mystery number? If I subtract 1 / 2 of it, then multiply by 3, and then add 2, the end result is 26.

Problem setup

It seems that this will have me hunt for a number that can solve an equation, as listed above.

Plans to Solve/Investigate the Problem

I will set up an equation to solve, and put in numbers until it solves correctly.

Investigation/Exploration of the Problem

At first, I tried this equation:

(x – X/2) times 3 + 2 = 26

Then I picked the number 6 and plugged it in.  (6 – 6/2) times 3 + 2 = 26

(6-3) 3 +2 = 26

18 * 3 + 2 = 26

54 + 2 not equal to 26

I tried several more numbers, then realized I had read the question incorrectly.  The correct equation should be:

((x/2) *3) + 2 = 26  This is because any number minus it’s half is the same as that number divided by 2.

I began plugging numbers in for x .  ((8/2) * 3) + 2 = 26;  (4 * 3) + 2 = 26; 12 + 2 is not equal to 26.  I realized that I could combine the 2 and the 26 on opposite sides of the equation, and then solve (x/2) * 3  =  24.  Then I realized I could solve x/2 to be equal to 8, because 8 * 3 = 24.  Therefore, “16” is the answer.

Extensions of the Problem

I could come up with my own mystery number, using 3 different operations.  I might try that some time.

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

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