Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

If $x$ and $y$ are positive integers with $3^{x} 5^{y} = 225$ , what is the value of $x + y$ ?

Your answer

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

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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