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. Mary’s 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?

Mary’s Cup-Filling Progress
Time (minutes)

0.5

1

1.5

2

2.5
Cups Remaining

99

81

63

45

27

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.

Answer 1

Mary is filling 36 cups per minute, which is faster than Jorge.

Explanation:

Answer 2

Mary is filling 36 cups per minute, which is faster than Jorge.

Explanation:

Lets get Jorge's time :

As the rate is constant, we can find the slope to know the number of cups he is filling per minute.

Slope is found using:
`(y2-y1)/(x2-x1)`

=
`(53-25)/(5-3)`

=
`(28)/(2)=14`

From the table lets get Mary's time:

`(99-81)/(1-0.5)`

=
`(18)/(0.5)=36`

Another data:
`(63-45)/(2-1.5)`

=
`(18)/(0.5)=36`

Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.

Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.