Question

MathWizard likes to play a fun number trick on her friends. She tells them to think of a number. She then tells them to subtract their number from 2 and multiply the result by 5. To this product she tells them to add half the difference when 24 is subtracted from 12 times their original number.
(a) If I use the number 8 and follow MathWizard's steps, what number will I get?
(b) If you correctly apply MathWizard's steps to your favorite number, and then tell MathWizard your result, how can MathWizard quickly figure out what number you started with?

Answer 1

Follow the steps for 8
(1) 8 * 2 = 16
(2) 16 * 5 = 80
Note: you could just combine the first 2 steps and multiply by 10 to start with. Much easier: just add a 0 onto 8.
(3a) 12 * 8 = 96
(3b)  96 - 24 = 72
(3c) So you want to take 1/2 72 which is 36
(4)   36 + 80 = 116

Let's try this  with x.
(2) x * 10 = 10x
(3) 1/2 (12*x - 24)
(3) 10x + 1/2 (12x - 24)
(3) 10x + 6x - 12
(4) 16x - 12

Problem B
Math wiz would add 12 to the number given to her and then divide by 16. That's pretty complicated to do quickly. 

For example Let the original number be 1221
(2) Multiply by 10 12210
(3) Take 1/2 the difference between 12 times 1221 and 24 which is 1/2(14652 - 24) = 7314
And add this result to 12210 
7314 + 12210 = 19524

Tell her the number. She has to add 12
19524 + 12 = 19536  And divide by 16
to get 1221. 
Pretty complex even for a wizard.