Question

jorge and mary are both filling cups with fruit punch in preparation for a party. after 3 minutes, jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. marys progress is shown in the table of values below. assuming that both jorge and mary are filling cups at a constant rate, which statement is correct?

marys cup-filling progress
\

$$\begin{tabular}{|c|c|c|c|c|c|} \\hline time (minutes) & 0.5 & 1 & 1.5 & 2 & 2.5 \\\\ \\hline cups remaining & 99 & 81 & 63 & 45 & 27 \\\\ \\hline \\end{tabular}$$

jorge is filling 14 cups per minute, which is faster than mary.
jorge is filling 28 cups per minute, which is faster than mary.
mary is filling 18 cups per minute, which is faster than jorge.
mary is filling 36 cups per minute, which is faster than jorge.

Explanation:

Find Jorge's filling rate

Using the Rate of Change knowledge point

$$
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The filling rate is \(14\) cups per minute.

Find Mary's filling rate

Using the Linear Equation from Table and Rate of Change knowledge points

$$
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$$

The filling rate is \(36\) cups per minute.

Compare the rates

Using the Rate of Change knowledge point

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Mary fills \(36\) cups per minute, which is faster than Jorge's rate of \(14\) cups per minute.

Answer:

• Jorge is filling 14 cups per minute, which is faster than Mary.
• Jorge is filling 28 cups per minute, which is faster than Mary.
• Mary is filling 18 cups per minute, which is faster than Jorge.
• Mary is filling 36 cups per minute, which is faster than Jorge. (Correct answer)