A: I am choosing an integer. I then subtract 10 from the integer, take the opposite of the result, add -3, and find the opposite of the new result. My result is -3. What is the original number?

Question

B: Judy wants to do the activity in part (a) with her classmates. Each classmate probably chooses a different number and Judy wants to tell each classmate quickly what number was chosen. Judy figures out that the only thing she needs to do is to add 7 to each answer she gets. Does this always work? Explain why or why not.
C: Come up with your own "trick" similar to the one in part (b) that works for each answer you get from your classmates.

Answer 1

A
n
n-10
10-n
7-n
n-7
n-7 = -3, so n=4

B yes, it always works, as shown above