Practice!

Sample Problem

The product of two integers is 24. What is largest, possible sum of the two numbers?

Solution

Let the two integers be a and b. We will list all possible cases for positive a and b.

Clearly, the largest sum occurs when a = 1 and b = 24, giving a sum of 25. Note that the largest sum occurs when the two variables are distanced as far apart from each other in the positive number line.