The Anysville Transit System (ATS) has four bus routes, as identified below: $\begin{array}{l}

\begin{array}{cc}
\text { Route }&\text { Average passengers }\
& \text { per day } \
1 & 682 \
2 & 2383 \
3 & 857 \
4 & 1425
\end{array}
\end{array}$
The ATS is replacing the entire old bus fleet with 35 new buses. Use the Webster method to determine how many buses each route should get.
A) 4, 14, 8, 9
B) 4, 15, 7, 9
C) 4, 16, 6, 9
D) 4, 16, 5, 10

Question

The Anysville Transit System (ATS) has four bus routes, as identified below: $\begin{array}{l}

\begin{array}{cc} 
\text { Route }&\text { Average passengers }\
& \text { per day } \
1 & 682 \
2 & 2383 \
3 & 857 \
4 & 1425
\end{array}
\end{array}$
The ATS is replacing the entire old bus fleet with 35 new buses. Use the Webster method to determine how many buses each route should get.
A) 4, 14, 8, 9
B) 4, 15, 7, 9
C) 4, 16, 6, 9
D) 4, 16, 5, 10

Quizplus · Accepted Answer

The Webster method is a method of apportionment used to allocate seats, resources, or in this case, buses, proportionally based on certain metrics, such as population or, as in this scenario, average passengers per day. To use the Webster method, you first calculate the standard divisor, which is the total number of units (in this case, passengers) divided by the total number of resources to be allocated (in this case, buses). Then, you calculate the initial allocation based on this divisor, adjust for any rounding issues, and ensure the total allocation matches the total resources available.1. Calculate the total number of passengers: $682 + 2383 + 857 + 1425 = 5347$.2. Calculate the standard divisor: $5347 \, \text{passengers} / 35 \, \text{buses} = 152.7714 \, \text{passengers/bus}$.3. Calculate the initial allocation (quotient) for each route by dividing the average passengers per day by the standard divisor, then round to the nearest whole number using the Webster method (which involves rounding at 0.5 and above):   - Route 1: $682 / 152.7714 = 4.465$, rounds to 4 buses.   - Route 2: $2383 / 152.7714 = 15.6$, rounds to 16 buses.   - Route 3: $857 / 152.7714 = 5.61$, rounds to 6 buses.   - Route 4: $1425 / 152.7714 = 9.33$, rounds to 9 buses.4. Check the total allocation: $4 + 16 + 6 + 9 = 35$ buses.The allocation matches the total number of buses available, so the correct distribution using the Webster method is 4, 16, 6, 9.

The Anysville Transit System (ATS) Has Four Bus Routes, as Identified