Problem of the Week
Problem A and Solution
Bus Stops

Problem

An empty bus starts its daily route. Along the way it makes several stops. At each stop, some passengers board the bus and some passengers exit the bus.

The table shows how many passengers get on and get off the bus at each stop.

1. How many passengers board the bus in total?

2. The bus has seats for \(30\) passengers. Once all the seats are full, passengers must stand. Between the 3^rd and 4^th stops, are there enough seats for all the passengers? If not, how many passengers must stand?

3. The bus gets a flat tire at the 6^th stop so all the passengers need to exit. How many passengers get off the bus at the 6^th stop?

Solution

1. The total number of passengers who board the bus is: \(23 + 17 + 13 + 1 + 2 = 56\).

2. The table summarizes the number of passengers on the bus after each stop.

   Stop Number	Number Boarding	Number Exiting	Total Passengers on the Bus
   \(1\)	\(23\)	\(0\)	\(23\)
   \(2\)	\(17\)	\(12\)	\(23 + 17 - 12 = 28\)
   \(3\)	\(13\)	\(3\)	\(28 + 13 - 3 = 38\)
   \(4\)	\(1\)	\(9\)	\(38 + 1 - 9 = 30\)
   \(5\)	\(2\)	\(8\)	\(30 + 2 - 8 = 24\)

   Thus, between the 3^rd and 4^th stops, there are \(38\) passengers on the bus. Since there are only \(30\) seats, there are not enough seats for all the passengers. The number of passengers who must stand is \(38 - 30 = 8\).

3. From the table in (b), we know that \(24\) passengers are on the bus when it arrives at the 6^th stop. They would all need to exit. Thus, \(24\) passengers get off the bus at the 6^th stop.