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UKMT Senior Mathematical Challenge, 2022

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The numbers $x$ and $y$ are such that $3^x + 3^{y+1} = 5\sqrt{3}$ and $3^{x+1} + 3^y = 3\sqrt{3}$ . What is the value of $3^x + 3^y$ ?

(A) $\sqrt{3}$ (B) $2\sqrt{3}$ (C) $3\sqrt{3}$ (D) $4\sqrt{3}$ (E) $5\sqrt{3}$

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