Question

A public transport bus leaves the terminal with 2/7 of its seats empty. When it reaches the first stop, 3/5 of the bus's capacity gets on and 1/4 gets off. At the next stop, 1/3 of the bus' total seating capacity gets off. Finally, at the third stop, 3/6 get on and 1/8 get off. Are there any seats left on the bus? What fraction of the passengers must travel standing?

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Answer to a math question A public transport bus leaves the terminal with 2/7 of its seats empty. When it reaches the first stop, 3/5 of the bus's capacity gets on and 1/4 gets off. At the next stop, 1/3 of the bus' total seating capacity gets off. Finally, at the third stop, 3/6 get on and 1/8 get off. Are there any seats left on the bus? What fraction of the passengers must travel standing?

Expert avatar
Jayne
4.4
96 Answers
1. Calculate the initial passengers on the bus:
\frac{5}{7}C

2. First stop changes:
- Passengers getting on: \frac{3}{5}C
- Passengers getting off: \frac{1}{4}C

New passenger count:
\frac{5}{7}C + \frac{3}{5}C - \frac{1}{4}C = \frac{149}{140}C

3. Second stop changes:
- Passengers getting off: \frac{1}{3}C

New passenger count:
\frac{149}{140}C - \frac{1}{3}C = \frac{307}{420}C

4. Third stop changes:
- Passengers getting on: \frac{3}{6}C = \frac{1}{2}C
- Passengers getting off: \frac{1}{8}C

Final passenger count:
\frac{307}{420}C + \frac{210}{420}C - \frac{52.5}{420}C = \frac{929}{840}C

5. Check for seats left and standing passengers:
- Total passengers are \frac{929}{840}C , which is greater than \( C \).

Fraction of passengers standing:
\frac{\frac{929}{840}C - C}{\frac{929}{840}C} = \frac{89}{929}

The bus is over capacity, and \( \frac{89}{929} \) of the passengers must stand.

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