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Algebra Difficulty 1.1 Junior Find the answer Canada

Two positive integers $x$ and $y$ have $xy=24$ and $x-y=5$ . The value of $x+y$ is

Pick one

Solution

The positive integer divisors of 24 are $1,2,3,4,6,8,12,24$ .

The pairs of divisors that give a product of $24$ are $24\times1$ , $12 \times 2$ , $8\times 3$ , and $6\times 4$ .

We want to find two positive integers $x$ and $y$ whose product is $24$ and whose difference is 5.

Since $8\times 3 = 24$ and $8-3=5$ , then $x=8$ and $y=3$ are the required integers.

Here, $x+y=8+3=11$ .

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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.