JAMB Mathematics 2010 Paper

Concept:When one quantity varies directly as another, it equals a constant multiplied by that quantity. Here, $y$ is directly proportional to the square root of $x$.Explanation:Write the variation equation as $y = k\sqrt{x}$, where $k$ is the constant of proportionality.Use the given pair $y = 3$ and $x = 16$ to find $k$.Substitute into the equation: $3 = k\sqrt{16}$.Since $\sqrt{16} = 4$, the equation becomes $3 = 4k$.Divide both sides by $4$ to get $k = \frac{3}{4}$.The direct variation formula is now $y = \frac{3}{4}\sqrt{x}$.To find $y$ when $x = 64$, first evaluate $\sqrt{64} = 8$.Then $y = \frac{3}{4} \times 8 = 6$.Answer:$y = 6$, so the correct option is B.