The week before a big concert, five friends (Alvin, Bert, Chip, Dennis, and Ethan) stood in line to buy tickets. There were other people between them, but the five friends were in line in the order listed above.
The line was really long, and they were pretty bored. Chip noticed that if he counted the number of strangers between each pair of friends, he got the numbers 7, 12.19, 21 36, 43, 55, 57, 64, and 76. Like I said, he was REALLY bored.
He sent the information to Ethan in a text message, and Ethan passed the time in line using Chip's information to determine how many people were between Alvin and Bert, between Bert and Chip, betwen Chip and Dennis, and between Dennis and Ethan. What did he find?
Since Chip is in the middle, we don't know if the interposed customers are in the respective order.
If they are, then it seems there are 7 between Alvin and Bert 12 between Bert and Chip, 19 between Alvin and Chip (counting or not counting Bert?) and so on.
With the above lack of data, I am not sure of my response.
To determine the number of people between each pair of friends, we can add up the numbers that Chip counted. Let's calculate:
7 + 12 + 19 + 21 + 36 + 43 + 55 + 57 + 64 + 76 = 390
Now, let's distribute these numbers between the pairs of friends:
Between Alvin and Bert: 7
Between Bert and Chip: 12 + 19 = 31
Between Chip and Dennis: 21 + 36 + 43 = 100
Between Dennis and Ethan: 55 + 57 + 64 + 76 = 252
Therefore, Ethan found that there were:
- 7 people between Alvin and Bert
- 31 people between Bert and Chip
- 100 people between Chip and Dennis
- 252 people between Dennis and Ethan.
To find out how many people were between the pairs of friends, let's follow the given information step by step:
1. We are given the numbers 7, 12, 19, 21, 36, 43, 55, 57, 64, and 76. These numbers represent the counts of strangers between each pair of friends.
2. First, let's find out how many people were between Alvin and Bert. The first number, 7, represents the count of strangers between Alvin and Bert. Therefore, there were 7 people between Alvin and Bert.
3. Next, let's find out how many people were between Bert and Chip. The second number, 12, represents the count of strangers between Bert and Chip. Since there were already 7 people between Alvin and Bert, we need to add 12 more people to get the total count between Bert and Chip. Therefore, there were 7 + 12 = 19 people between Bert and Chip.
4. Continuing in the same pattern, let's find out how many people were between Chip and Dennis. The third number, 19, represents the count of strangers between Chip and Dennis. Since there were already 19 people between Bert and Chip, we need to add 19 more people to get the total count between Chip and Dennis. Therefore, there were 19 + 19 = 38 people between Chip and Dennis.
5. Finally, let's find out how many people were between Dennis and Ethan. The fourth number, 21, represents the count of strangers between Dennis and Ethan. Since there were already 38 people between Chip and Dennis, we need to add 21 more people to get the total count between Dennis and Ethan. Therefore, there were 38 + 21 = 59 people between Dennis and Ethan.
In summary, Ethan found that there were:
- 7 people between Alvin and Bert.
- 19 people between Bert and Chip.
- 38 people between Chip and Dennis.
- 59 people between Dennis and Ethan.