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A cherry pitting machine pits 12 pounds of cherries in 3 minutes. At this rate, how many minutes does it take the machine to pit 96 pounds of cherries?

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A cherry pitting machine pits 12 pounds of cherries in 3 minutes. At this rate, how many minutes does it take the machine to pit 96 pounds of cherries?

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Choice C is correct. It's given that the cherry pitting machine pits $12$ pounds of cherries in $3$ minutes. This rate can be written as $\\frac{12\\text{ pounds of cheries}}{3\\text{ minutes}}$. If the number of minutes it takes the machine to pit $96$ pounds of cherries is represented by $x$, the value of $x$ can be calculated by solving the equation $\\frac{12\\text{ pounds of cherries}}{3\\text{ minutes}}=\\frac{96\\text{ pounds of cherries}}{x\\text{ minutes}}$, which can be rewritten as $\\frac{12}{3}=\\frac{96}{x}$, or $4=\\frac{96}{x}$. Multiplying each side of this equation by $x$ yields $4x=96$. Dividing each side of this equation by $4$ yields $x=24$. Therefore, it takes the machine $24$ minutes to pit $96$ pounds of cherries.

Choice A is incorrect. This is the number of minutes it takes the machine to pit $32$, not $96$, pounds of cherries.

Choice B is incorrect. This is the number of minutes it takes the machine to pit $60$, not $96$, pounds of cherries.

Choice D is incorrect. This is the number of minutes it takes the machine to pit $144$, not $96$, pounds of cherries.

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A cherry pitting machine pits 12 pounds of cherries in 3 minutes. At this rate, how many minutes does it take the machine to pit 96 pounds of cherries?

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