NP Chapter 1 Page 39 Exercise 35

[ray_serrano]

Why are we multiplying the remainder of x by 5 and then subtracting the remainder of y to get to 18.

[JonathanSchneider]

We are asked about 5x - y. Thus, the x value will be multiplied by 5. If the x value leaves a remainder of 5 (when divided by 9), then 5x will have five of those remainders, for a total remainder of 25. But we must subtract the y value also. This y value has a remainder of 7. Thus, we will have a total remainder of 25 - 7, or 18.