If $50$ one-cent jcoins were stacked on top of each other in a column, the column would be approximately $3 \frac{7}{8}$ inches tall. At this rate, which of the following is closest to the number of one-cent coins it would take to make an $8$ -inch-tall column? $\newline$ A) $75$ $\newline$ B) $100$ $\newline$ C) $200$ $\newline$ D) $390$

Full solution

Q. If

50

one-cent jcoins were stacked on top of each other in a column, the column would be approximately

3 \frac{7}{8}

inches tall. At this rate, which of the following is closest to the number of one-cent coins it would take to make an

8

-inch-tall column?

\newline

75

\newline

100

\newline

200

\newline

390

Calculate coin height: Calculate the height of one coin. $\newline$ Height of $50$ coins = $3\left(\frac{7}{8}\right)$ inches. $\newline$ Convert $3\left(\frac{7}{8}\right)$ to an improper fraction: $3\left(\frac{7}{8}\right) = \left(\frac{24}{8}\right) + \left(\frac{7}{8}\right) = \frac{31}{8}$ inches. $\newline$ Height of one coin = $\frac{31}{8} / 50 = \frac{31}{400}$ inches per coin.
Calculate coins for $8$ -inch column: Calculate the number of coins needed for an $8$ -inch column. $\newline$ Number of coins = $8 \text{ inches} / \left(\frac{31}{400}\right) \text{ inches per coin}.$ $\newline$ Simplify the division: $8 \times \left(\frac{400}{31}\right) = \frac{3200}{31} \approx 103.23$ .
Round to nearest option: Round to the nearest option. $\newline$ The closest options are $100$ or $200$ . $\newline$ Since $103.23$ is closer to $100$ , choose $100$ .