If 100 five-cent coins were stacked on top of each other in a column, the column would be approximately \(6\dfrac{5}{8}\) inches tall. At this rate, which of the following is closest to the number of five-cent coins it would take to make an \(15\)-inch-tall column?

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We can set up a simple proportion:

$$ \frac{100 \text{ coins}}{6 \frac{5}{8} \text{ inches}}= \frac{x \text{ coins}}{15 \text{ inches}} $$ $$ 6 \frac{5}{8} \cdot x = 15 \cdot 100 $$ $$ x \approx \boxed{226} \text{ coins} $$