CEMC Cayley

Algebra Difficulty 2.0 Junior Find the answer

What is the largest possible value for $n$ if the average of the two positive integers $m$ and $n$ is 5?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Since the average of $m$ and $n$ is 5, then $\frac{m+n}{2}=5$ which means that $m+n=10$ . In order for $n$ to be as large as possible, we need to make $m$ as small as possible. Since $m$ and $n$ are positive integers, then the smallest possible value of $m$ is 1, which means that the largest possible value of $n$ is $n=10-m=10-1=9$ .

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