Question

As part of a "green" initiative, California wants to apportion 150 new electric vehicles toits university system campuses. Given the following table, use the Webster method todetermine how many of the vehicles should be apportioned to the Davis campus basedon the number of students.

Answer 1

We are given a table of values showing three campuses and their corresponding student enrollment. The required solution is an apportionment of 150 vehicles to all campuses and specifically, Davis campus.

Let us begin by taking the step by step procedure. The parameter to be used is the student enrollment since the question states that the vehicles should be apportioned based on the number of students.

First of all we shall calculate the total number of students enrolled and that would be;

`32290+2700+18140=53130`

We shall divide this figure by the number of vehicles to be apportioned and that gives us the standard divisor;

`\begin{gathered} \text{Standard divisor}=(53130)/(150)=354.2 \\ \text{Modified divisor}=354.2 \end{gathered}`

Next step, we shall divide each data given by the modified divisor, as shown;

`\begin{gathered} (32290)/(354.2)=91.1631\approx91 \\ (2700)/(354.2)=7.6228\approx8 \\ (18140)/(354.2)=51.2140\approx51 \end{gathered}`

Observe carefully that the results from the division using our modified divisor yields answers that are not integers, that is, the answers includes some decimals. We now have to approximate each answer to the nearest whole number. This is simply because, the electric cars cannot possibly come in fractions. Hence for the results, the approximate values are;

91.1631 (rounded down to 91)

7.6228 (rounded up to 8)

51.2140 (rounded down to 51)

This shows that the Davis campus would be allocated 91 vehicles if the Webster method is used to allocate 150 vehicles. If all three numbers are added up, the result should be 150, that is;

`91+8+51=150`

With that, we do not need to calculate any further.

ANSWER:

The Davis campus gets 91 electric vehicles.