All 41 people are standing in a row, facing north. Juno is 23rd from the right end, while Cherry is 31st from the left end. How many people are there between Juno and Cherry?
11
Calculating People Between Juno and Cherry in a Row
This problem involves finding the number of people situated between two individuals, Juno and Cherry, whose positions are given from opposite ends of a row. We are given the total number of people and their positions.
Information Provided:
- Total number of people in the row: 41
- All people are facing North.
- Juno's position: 23rd from the right end.
- Cherry's position: 31st from the left end.
Step 1: Find Juno's Position from the Left End
To find the number of people between Juno and Cherry, it's helpful to know both their positions relative to the same end (either left or right). Since Cherry's position is given from the left, let's find Juno's position from the left.
The formula to find the position from the left end is:
Position from Left = Total People - Position from Right + 1
Applying this to Juno:
Juno's position from left = \(41 - 23 + 1\)
Juno's position from left = \(18 + 1 = 19\)
So, Juno is the 19th person from the left end.
Step 2: Find Cherry's Position from the Right End
Similarly, we can find Cherry's position from the right end, although it's not strictly necessary if we use the left positions.
The formula to find the position from the right end is:
Position from Right = Total People - Position from Left + 1
Applying this to Cherry:
Cherry's position from right = \(41 - 31 + 1\)
Cherry's position from right = \(10 + 1 = 11\)
So, Cherry is the 11th person from the right end.
Step 3: Calculate the Number of People Between Juno and Cherry
Now we know:
- Juno is 19th from the left.
- Cherry is 31st from the left.
Since Cherry (31st from left) is further down the row from Juno (19th from left), we can calculate the number of people between them.
Number of people between = (Position of the person from left who is further down) - (Position of the other person from left) - 1
Number of people between = \(31 - 19 - 1\)
Number of people between = \(12 - 1 = 11\)
Alternative Method using Right Positions:
We know:
- Juno is 23rd from the right.
- Cherry is 11th from the right.
Since Juno (23rd from right) is further down the row (from the right end perspective) than Cherry (11th from right), we calculate:
Number of people between = (Position of the person from right who is further down) - (Position of the other person from right) - 1
Number of people between = \(23 - 11 - 1\)
Number of people between = \(12 - 1 = 11\)
Conclusion
Both methods confirm that there are 11 people standing between Juno and Cherry.
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