22
Total Students in Row: Using Priya's Position
This problem requires us to find the total number of students in a single row. We are given Priya's position counted from both the left end and the right end of the row.
Understanding Priya's Placement
The specific details provided about Priya's position are:
- Priya's position from the left side of the row is $9^{th}$.
- Priya's position from the right side of the row is $14^{th}$.
Method for Calculating Total Students
To determine the total number of students, we can add the number of students Priya is positioned relative to from both ends. Priya's position from the left includes all students from the start up to and including Priya. Similarly, her position from the right includes all students from the end up to and including Priya.
Since Priya is counted in both positional counts, we must subtract 1 from the sum of her positions to avoid counting her twice. The formula is:
Total Students = (Priya's Position from Left) + (Priya's Position from Right) - 1
Step-by-Step Calculation
Let's apply the formula with the given numbers:
- Priya's position counted from the left = $9$.
- Priya's position counted from the right = $14$.
- Add these two positions together: $9 + 14$.
- The sum equals $23$.
- Subtract 1 to correct for counting Priya twice: $23 - 1$.
- The final result is $22$.
Thus, there are exactly 22 students in the row.
Alternative Perspective
We can also visualize the row based on Priya:
- The number of students to Priya's left is her position from the left minus 1 (Priya herself). So, $9 - 1 = 8$ students are to her left.
- The number of students to Priya's right is her position from the right minus 1 (Priya herself). So, $14 - 1 = 13$ students are to her right.
- The total number of students is the sum of students to her left, Priya herself, and students to her right.
- Total Students = (Students to the left) + Priya + (Students to the right)
- Total Students = $8 + 1 + 13 = 22$.
This confirms the total number of students in the row is 22.
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