Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.7 Junior Find the answer

Given that the ratio of $3x - 4$ to $y + 15$ is constant, and $y = 3$ when $x = 2$ , then, when $y = 12$ , $x$ equals:

Pick one

Solution

Let $k$ be the constant ratio. Then $k = \frac{3(2)-4}{(3)+15} = \frac{1}{9} = \frac{3x - 4}{(12) + 15}$ . Solving gives $3x - 4 = 3 \Longrightarrow x = \frac 73 \Rightarrow \mathrm{(B)}$ .

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