Chapter 5.1, Problem 9MC

a. I chose 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?

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 (a).