Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

He notices that he has as many people in front of him as behind him. He sees two friends, both standing behind him in the line, one in 19th place and the other in 28th place.  In which position in the line is Martin? Let's start off by labeling Martin. He is one person, and let's say the people in front and behind are X people,  since we know that he is in the middle. Next, we can write this out as 2X plus 1, as the number of people in the line. Now, if we take a look at our option A, 14, we can call X 13.  We do this because Martin will be in 14th place, meaning there are 13 people in front of him, and since we know that there are the same amount of people behind him,  there are also 13 people behind him. This would mean there would be 27 people. While this is a multiple of 3, it does make it impossible,  since we know one of Martin's friends is in 28th place, so there have to be more people, so A cannot be the answer. Next, we will try option B.  When we do this, we get 29, which is not a multiple of 3, so this cannot be the answer. Next, we will try C. Again, not a multiple of 3, so this cannot be an answer.  And finally, when we try Martin in 17th place, we do get 33, which is a multiple of 3 and has enough people so that his friends can be in 19th and 28th place,  so the answer will be D, 17.

Video Summary

Summary Not Available