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Bus headcount equality after a stop: Find the initial total number of passengers. Initially, women count = half the men count. At city Y, 10 men alight and 5 women board; then men and women become equal. Compute the number of passengers at the beginning. Choose the correct total.

Q: Bus headcount equality after a stop: Find the initial total number of passengers. Initially, women count = half the men count. At city Y, 10 men alight and 5 women board; then men and women become equal. Compute the number of passengers at the begi…

Variables Let initial men = m, women = w with w = m/2. After city Y: men = m − 10, women = w + 5 = m/2 + 5; these are equal. Equation m − 10 = m/2 + 5 ⇒ m/2 = 15 ⇒ m = 30Then w = m/2 = 15. Initial total m + w = 30 + 15 = 45. Final Answer 45

Difficulty: Easy

Correct Answer: 45

Explanation:

Variables

Let initial men = m, women = w with w = m/2.
After city Y: men = m − 10, women = w + 5 = m/2 + 5; these are equal.

Equation
m − 10 = m/2 + 5 ⇒ m/2 = 15 ⇒ m = 30Then w = m/2 = 15.

Initial total
m + w = 30 + 15 = 45.

Final Answer
45

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