Final answer:
To find the largest of the three positive whole numbers that add to 96 and have the sum of any two divisible by the third, we can start by considering the possibilities. By trying different values of a, b, and c, we find that the largest of the three numbers is 49.
Step-by-step explanation:
To find the largest of the three positive whole numbers that add to 96 and have the sum of any two divisible by the third, we can start by considering the possibilities. Let's call the three numbers a, b, and c. We know that a + b + c = 96. We also know that (a + b) % c = 0, (a + c) % b = 0, and (b + c) % a = 0. Using these equations, we can solve for the possible values of a, b, and c until we find the largest one.
Let's start by considering the case where a is the largest number. Since any two numbers sum must be divisible by the third, we can set up the equation (a + b) % c = 0. Substituting the values we know, we get (a + b) % (96 - a - b) = 0. Using this equation, we can solve for a, b, and c until we find the largest one. The same process can be repeated for cases where b or c is the largest number.
By trying different values of a, b, and c, we find that the largest of the three numbers is 49.