Question

2. MOVIE LINE A bunch of people were standing in line for a movie. Averi got there late, and realized that she knew every person in line. She decided not to get in line until she figured out who to cut in with. She first stopped and talked to Jake, who was at the back of the line. Then she moved forward by passing 3 people and talked to Alexandra. She then moved forward again by passing 9 people and talked to Walter. Then she moved backward by passing 4 people and talked to Annie. Then she moved forward by passing 12 people and talked DRAW A DIAGRAM to Katie. Finally she moved backward by passing 2 people and joined Carli in line. Carli was originally the person in the exact middle of the line. Including Averi (who was now in line) how many people are in the line? Note: Moving forward refers to moving toward the front of the line and moving backward refers to moving toward the back of the line. 1 BACKBOARD

Answer 1

Let's describe the situation -

Averi first was with Jake, who was at the back.

Alexendria is 4 position before Jake as there are 3 people between them.

Walter is 10 position before Alexendria as there are 9 people between them.

Annie is 5 position after Walter as there are 4 people between them.

Katie is 13 position before Annie as there are 12 people between them.

Carli is 3 position after Katie as there are 2 people between them.

Suppose, there were n people in line. So, Jake was at position n.

n is odd as there is an exact middle. The position of Carli was (n+1)/2

Now, from the above, we get (n+1)/2=n-4-10+5-13+3=n-19

n+1=2n-38

n=39

So, including Averi, there are 39+1=40 people in the line.