sat-dog

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 $\frac{12 \text{pounds} \text{of} \text{cherries}}{3 \text{minutes}}$. 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 $\frac{12 \text{pounds} \text{of} \text{cherries}}{3 \text{minutes}}=\frac{96 \text{pounds} \text{of} \text{cherries}}{x \text{minutes}}$, 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.