SAT Question fe1ec415: Ratios Rates Proportional Relationships And Units answer and explanation with Desmos solution

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