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} & $\begin{array}{c}\text { Votes for Republican } \\ \text { candidates (1000s) }\end{array}$ & $\begin{array}{c}\text { Votes for Democratic } \\ \text { candidates (1000s) }\end{array}$ & Republican seats & Democratic seats \\ \hline $\mathbf{2 0 1 0}$ & 1925 & 1669 & 11 & 3 \\ $\mathbf{2 0 1 2}$ & 2525 & 2465 & 12 & 4 \\ \hline \end{tabular} a. Find the percentages of votes cast for Republican and Democratic House candidates in 2010 and 2012. 2010: Republican $53.6 \%$ Democrat $46.4 \%$ 2012: Republican $50.6 \%$ Democrat $49.4 \%$ (Round to one decimal place as needed.) b. Find the percentages of House seats that were won by Republican and Democratic candidates in 2010 and 2012. $\begin{array}{lll}\text { 2010: } & \text { Republican } \square \% & \text { Democrat } \square \% \\ \text { 2012: } & \text { Republican } \square \% & \text { Democrat } \square \%\end{array}$ (Type an integer or decimal rounded to one decimal place as needed.)
Solution
Step 1 ：Given the number of seats won by each party in 2010 and 2012, we can calculate the percentage of seats won by each party by dividing the number of seats won by the total number of seats and multiplying by 100.
Step 2 ：For 2010, the number of Republican seats is 11 and the number of Democratic seats is 3. The total number of seats is 14.
Step 3 ：Calculate the percentage of seats won by Republicans in 2010: \(\frac{11}{14} \times 100 = 78.6\%\)
Step 4 ：Calculate the percentage of seats won by Democrats in 2010: \(\frac{3}{14} \times 100 = 21.4\%\)
Step 5 ：For 2012, the number of Republican seats is 12 and the number of Democratic seats is 4. The total number of seats is 16.
Step 6 ：Calculate the percentage of seats won by Republicans in 2012: \(\frac{12}{16} \times 100 = 75.0\%\)
Step 7 ：Calculate the percentage of seats won by Democrats in 2012: \(\frac{4}{16} \times 100 = 25.0\%\)
Step 8 ：Final Answer: \(\boxed{\text{2010: Republican 78.6\%, Democrat 21.4\%}}\)
Step 9 ：Final Answer: \(\boxed{\text{2012: Republican 75.0\%, Democrat 25.0\%}}\)
