Problem

West End school district is purchasing 50 new computers to be distributed among the five schools in the district. The computers will be apportioned based on the school population of each school as given in the table below. Use Jefferson's method to apportion the computers.
\begin{tabular}{l|ccccc}
School & a & b & c & d & e \\
\hline Population & 210 & 165 & 160 & 175 & 190
\end{tabular}
A.
\begin{tabular}{l|ccccc}
School & a & b & c & d & e \\
\hline Number of Computers & 12 & 9 & 10 & 10 & 9
\end{tabular}
B. School
\begin{tabular}{l|ccccc}
School & a & b & c & d & e \\
\hline Number of Computers & 12 & 9 & 9 & 10 & 10
\end{tabular}
C.
\begin{tabular}{l|ccccc}
School & a & $b$ & $c$ & $d$ & $e$ \\
\hline Number of Computers & 11 & 10 & 9 & 10 & 10
\end{tabular}
D.
\begin{tabular}{l|c|cccc}
School & $a$ & $b$ & $c$ & $d$ & $e$ \\
\hline Number of Computers & 11 & 9 & 10 & 10 & 10
\end{tabular}

Answer

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Answer

\(\boxed{\text{Final Answer: School a gets 14 computers, school b gets 9 computers, school c gets 9 computers, school d gets 10 computers, and school e gets 11 computers.}}\)

Steps

Step 1 :Calculate the total population by adding the population of each school: \(210 + 165 + 160 + 175 + 190 = 900\).

Step 2 :Calculate the standard divisor by dividing the total population by the total number of computers to be distributed: \(\frac{900}{50} = 18\).

Step 3 :Calculate the initial quotas by dividing the population of each school by the standard divisor and rounding down to the nearest whole number: \([\frac{210}{18}, \frac{165}{18}, \frac{160}{18}, \frac{175}{18}, \frac{190}{18}] = [14, 9, 8, 9, 10]\).

Step 4 :Sum up the initial quotas to get the initial apportionment: \(14 + 9 + 8 + 9 + 10 = 47\).

Step 5 :Calculate the remaining computers to be distributed by subtracting the initial apportionment from the total number of computers: \(50 - 47 = 3\).

Step 6 :Distribute the remaining computers one at a time to the schools with the largest fractional parts of their quotas. The final apportionment of computers according to Jefferson's method is \([14, 9, 9, 10, 11]\).

Step 7 :\(\boxed{\text{Final Answer: School a gets 14 computers, school b gets 9 computers, school c gets 9 computers, school d gets 10 computers, and school e gets 11 computers.}}\)

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