Question

Tyler says he invented a number puzzle.

He asks Clare to pick a number, and then asks her to do the following:



Triple the number



Subtract 7

Double the result



Subtract 22



Divide by 6



Clare says her final answer is -3. Tyler says her original number she thought must have been 3.



How did Tyler know that? Explain or show your reasoning.

Answer 1

If Clare’s original number was 3 then she would first triple the number
3*3 is 9
Subtract 7 from 9 and you get 2
2 doubled is 4
22 subtracted from 4 is -18
-18 divided by 6 is -3
So Tyler just took Clare’s final answer (-3) and did the opposite if the steps back words
(multiple by 6, add 22, divide by 2, add 7, divide by 3)