Problem

The 2010 census led to the loss of two House seats in State A and State B, the loss of one House seat in State C, the gain of two House seats in State D, and the gain of four House seats in State E. Consider the following approximate vote counts for all House districts in these states in 2010 (before redistricting) and 2012 (after redistricting). The figure is in thousands of votes. Votes for other parties are neglected. Complete parts (a) through (d) below.
\begin{tabular}{ccccc}
& \begin{tabular}{c}
Votes for Republican \\
candidates (1000s)
\end{tabular} & \begin{tabular}{c}
Votes for Democratic \\
candidates (1000s)
\end{tabular} & Republican seats & Democratic seats \\
\hline 2010 & 2089 & 1637 & 16 & 8 \\
2012 & 2664 & 2403 & 17 & 9 \\
\hline & & & & \\
\hline
\end{tabular}
a. Find the percentages of votes cast for Republican and Democratic House candidates in 2010 and 2012.
2010: Republican $\square \%$
Democrat $\square \%$
2012: Republican $\square \%$
Democrat $\square \%$
(Round to one decimal place as needed.)

Answer

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Answer

So, the percentages of votes cast for Republican and Democratic House candidates in 2010 and 2012 are: 2010: Republican \(\boxed{56.1\%}\), Democrat \(\boxed{43.9\%}\) and 2012: Republican \(\boxed{52.6\%}\), Democrat \(\boxed{47.4\%}\). These values are rounded to one decimal place as needed.

Steps

Step 1 :Given the votes for Republican and Democratic candidates in 2010 and 2012, we need to find the percentage of votes cast for each party in both years.

Step 2 :In 2010, the total votes cast were 2089 thousand for Republicans and 1637 thousand for Democrats, making a total of 3726 thousand votes.

Step 3 :In 2012, the total votes cast were 2664 thousand for Republicans and 2403 thousand for Democrats, making a total of 5067 thousand votes.

Step 4 :To find the percentage of votes for each party, we divide the votes for that party by the total votes and multiply by 100.

Step 5 :For 2010, the percentage of votes for Republicans is \((2089 / 3726) \times 100 = 56.1\% \) and for Democrats is \((1637 / 3726) \times 100 = 43.9\%\).

Step 6 :For 2012, the percentage of votes for Republicans is \((2664 / 5067) \times 100 = 52.6\% \) and for Democrats is \((2403 / 5067) \times 100 = 47.4\%\).

Step 7 :So, the percentages of votes cast for Republican and Democratic House candidates in 2010 and 2012 are: 2010: Republican \(\boxed{56.1\%}\), Democrat \(\boxed{43.9\%}\) and 2012: Republican \(\boxed{52.6\%}\), Democrat \(\boxed{47.4\%}\). These values are rounded to one decimal place as needed.

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