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Algebra Difficulty 1.2 Junior Find the answer Canada

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

$5$
$7$
$9$
$11$
$13$

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 $\dfrac{m+n}{2} = 5$ 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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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.