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Number theory Difficulty 1.3 Junior Find the answer Canada

If $x$ and $y$ are positive integers with $3^x 5^y = 225$ , then $x + y$ equals

Pick one

Solution

Since $15^2=225$ and $15 = 3\cdot 5$ , then $225=15^2=(3\cdot 5)^2 = 3^2 \cdot 5^2$ .

Therefore, $x=2$ and $y=2$ , so $x+y=4$ .

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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.