Problem

The legislature in a state has 42 seats. Apportion these seats to the six counties below using Webster's method.
\begin{tabular}{|l|l|l|}
\hline County & Population & Seats Received \\
\hline Adams & 474,000 & \\
\hline Grant & 472,000 & \\
\hline Colton & 192,000 & \\
\hline Davis & 333,000 & \\
\hline Hayes & 327,000 & \\
\hline McKinley & 473,000 & \\
\hline
\end{tabular}
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\(\boxed{\text{Final allocation:}}\) \(\text{Adams:} 9\) \(\text{Grant:} 9\) \(\text{Colton:} 3\) \(\text{Davis:} 6\) \(\text{Hayes:} 6\) \(\text{McKinley:} 9\)

Steps

Step 1 :\(\text{Total population} = 474,000 + 472,000 + 192,000 + 333,000 + 327,000 + 473,000 = 2,271,000\)

Step 2 :\(\text{Standard divisor} = \frac{\text{Total population}}{\text{Total seats}} = \frac{2,271,000}{42} = 54,071.43\)

Step 3 :\(\text{Initial quotas} = \frac{\text{Individual population}}{\text{Standard divisor}}\) \(\text{For Adams:} \frac{474,000}{54,071.43} = 8.76\) \(\text{For Grant:} \frac{472,000}{54,071.43} = 8.72\) \(\text{For Colton:} \frac{192,000}{54,071.43} = 3.55\) \(\text{For Davis:} \frac{333,000}{54,071.43} = 6.16\) \(\text{For Hayes:} \frac{327,000}{54,071.43} = 6.04\) \(\text{For McKinley:} \frac{473,000}{54,071.43} = 8.74\)

Step 4 :\(\text{Initial seats allocation} = \text{Integer part of quotas}\) \(\text{For Adams:} 8\) \(\text{For Grant:} 8\) \(\text{For Colton:} 3\) \(\text{For Davis:} 6\) \(\text{For Hayes:} 6\) \(\text{For McKinley:} 8\) \(\text{Total seats allocated:} 39\)

Step 5 :\(\text{Remaining seats} = \text{Total seats} - \text{Total seats allocated} = 42 - 39 = 3\) \(\text{These are allocated to the constituencies with the highest fractional parts of their quotas. In this case, these are Adams, Grant, and McKinley, each receiving one additional seat.}\)

Step 6 :\(\boxed{\text{Final allocation:}}\) \(\text{Adams:} 9\) \(\text{Grant:} 9\) \(\text{Colton:} 3\) \(\text{Davis:} 6\) \(\text{Hayes:} 6\) \(\text{McKinley:} 9\)

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