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

This is an easy problem to solve if we look at it algebraically. We need re-write this problem using numbers and symbols.


Investigation/Exploration of the Problem

Let's call the mystery number x.

We now that  we need to subtract 1/2 of the mystery number. We can write this as .5x. We need to multiply .5x by 3 then add 2 and the result is 26.

 So our problem written algebraically is


                                        (.5x)3 + 2 = 26


Now we just need to solve for x to get the mystery number.


          First we simplify: (.5x)3 + 2 = 26

          and the result is   1.5 x + 2 = 26

 We now subtract 2 from both sides and the result is

                                        1.5x = 24

                                          x = 16


We can check to see if we are correct by plugging 16 into the problem. If we subtract half of 16 we are left with 8. 8 times 3 is equal to 24 and 24 + 2 = 26.


 Author & Contact
Laura Thomas

Memorial Middle School