2012 AMC 10A Problems/Problem 8
Problem 8
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?
Solution
Let the three numbers be equal to , , and . We can now write three equations:
Adding these equations together, we get that
and
Substituting the original equations into this one, we find
Therefore, our numbers are 12, 7, and 5. The middle number is