Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it. A Table titled Test Time, showing Number of Questions, Time per Item in minutes, and Total Time in minutes. The first row shows Multiple Choice, with m, 3, and 3 m. The second row shows Free Response, with 15 minus m, 8, and x. The third row shows Total, with 15, blank, and 55. Which value could replace x in the table? 7 – m 23 – m 8(15 – m) 8(15) – m

Question

01-05-2024
Mathematics

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Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it. A Table titled Test Time, showing Number of Questions, Time per Item in minutes, and Total Time in minutes. The first row shows Multiple Choice, with m, 3, and 3 m. The second row shows Free Response, with 15 minus m, 8, and x. The third row shows Total, with 15, blank, and 55. Which value could replace x in the table? 7 – m 23 – m 8(15 – m) 8(15) – m

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Xaioo Xaioo · Answer 1 · 2024-05-01T10:12:27+02:00

Answer:

[tex][/tex] To find the value that could replace x in the table, we need to first determine the total time for the Free Response questions.

Total time for Multiple Choice questions = Number of Multiple Choice questions [tex] \times[/tex] Time per item

Total time for Multiple Choice questions = m [tex] \times[/tex] 3 = 3m

Total time for Free Response questions = Number of Free Response questions [tex] \times[/tex] Time per item

Total time for Free Response questions = (15 - m)[tex] \times[/tex]8 = 8(15 - m)

Now, we know the Total Time for the test is 55 minutes. So, the total time for both Multiple Choice and Free Response questions should add up to 55 minutes.

Total time for Multiple Choice questions + Total time for Free Response questions = Total Time for the test

3m + 8(15 - m) = 55

3m + 120 - 8m = 55

-5m = -65

m = 13

Now, we can substitute m = 13 into the equation for the Total Time for Free Response questions:

8(15 - 13) = 8(2) = 16

Therefore, the value that could replace x in the table is 16.