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Zorluk: OrtaOrder and Ranking

In a single-file queue of passengers waiting to board a ferry, Oliver is standing 14th14^{\text{th}} from the front and Maya is standing 29th29^{\text{th}} from the back. If Oliver and Maya completely interchange their positions, Maya becomes 37th37^{\text{th}} from the back. How many passengers are standing in the queue?

  1. 50Cevap
  2. B
    51
  3. C
    42
  4. D
    65

Cevap

There are 50 passengers in the queue.
Upon interchanging positions, Maya occupies Oliver's original spot. This specific spot in the queue is 14th14^{\text{th}} from the front (established by Oliver) and 37th37^{\text{th}} from the back (established by Maya's new rank). Adding these two directional ranks and subtracting 11 (to correct for double-counting the person in that exact spot) yields exactly 5050 passengers.

Adım Adım Çözüm

1
Analyze the positional interchange.
Maya moves to Oliver's original position.
When two people swap places, the physical position in the queue remains constant while the occupants change.
2
Determine the dual rank of the shared position.
The position is 14th14^{\text{th}} from the front (Oliver's old rank) and 37th37^{\text{th}} from the back (Maya's new rank).
To find the total number of people, we need the exact rank of a single specific spot from both ends of the queue.
3
Apply the total queue length formula.
Total =(Position from front)+(Position from back)−1= (\text{Position from front}) + (\text{Position from back}) - 1
Adding the two ranks counts the person at that specific spot twice, so 11 must be subtracted to get the accurate total.
4
Calculate the final total.
14+37−1=5014 + 37 - 1 = 50
Direct mathematical substitution provides the total count.

Anahtar Kavram

Positional Interchange and Dual Rank Calculation

Alternatif Yöntem

Find the total positional shift: Maya moved from 29th29^{\text{th}} from the back to 37th37^{\text{th}} from the back, an 88-position leap forward. Since she took Oliver's spot (14th14^{\text{th}} from the front), Oliver was 88 positions ahead of her original spot. Her original spot from the front was 14+8=22nd14 + 8 = 22^{\text{nd}}. Therefore, the total is her original front rank (2222) plus her original back rank (2929) minus 11, which equals 5050.
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