Problem 36 - Algebra 1: Concepts and Skills

Question

The table below shows the number of electoral votes each candidate in the Election of 1860 received. What percent of the total number of electoral votes did each candidate receive? $$ \begin{array}{|c|c|c|} \hline {\text { Party }} & {\text { Candidate }} & {\text { Electoral votes }} \\\ \hline \text { Republican } & {\text { Abraham Lincoln }} & {180} \\ \hline \text { Southern Democratic } & {\text { J.C. Breckinridge }} & {72} \\\ \hline \text { Constitutional Union } & {\text { John Bell }} & {39} \\ \hline \text { Northern Democratic } & {\text { Stephen Douglas }} & {12} \\ \hline \end{array} $$

Step-by-Step Solution

Answer

Abraham Lincoln got approximately 59.41 percent of the total electoral votes, J.C. Breckinridge got approximately 23.76 percent, John Bell got approximately 12.87 percent, and Stephen Douglas got approximately 3.96 percent.

Step 1: Determine the Total Number of Electoral Votes

We add up the numbers of electoral votes from each candidate to get the total. This is from the information given in the problem: \(180 + 72 + 39 + 12 = 303\) electoral votes in total.

Step 2: Calculating the Percentage for each Candidate

For each candidate, we divide the number of votes they received by the total number of votes, then multiply by 100 to convert the result to a percentage. For example, for Abraham Lincoln, it would be \((180 / 303) * 100 \% \), which gives approximately \(59.41 \% \). Repeat this calculation for each candidate.

Step 3: Repeating Calculations for All Candidates

We do the same calculation for all the candidates: for J.C. Breckinridge, get \((72 / 303) * 100 \% \, \approx 23.76 \% \). For John Bell, do \((39 / 303) * 100 \% \, \approx 12.87 \% \). And finally, for Stephen Douglas, \((12 / 303) * 100 \% \, \approx 3.96 \% \)

Key Concepts

Electoral Votes

Electoral votes are crucial in determining the outcome of United States presidential elections. Unlike a popular vote, where the candidate with the most votes nationwide wins, electoral votes determine the winner.

Here's how it works:

• Each state is assigned a number of electoral votes based on its representation in Congress, which equals the sum of its Senators and Representatives.
• When citizens cast their vote for a presidential candidate, they are actually voting for a slate of electors pledged to that candidate.
• The candidate who receives the majority of the electoral votes becomes the President.

In the 1860 election, as detailed, Abraham Lincoln received a significant portion of the electoral votes, shaping the future of the country.

Mathematical Operations

To solve percentage problems, like finding out what percent of the total electoral votes each candidate received, you need basic mathematical operations. Here's how to calculate percentages step-by-step:

• First, determine the total quantity. In our example, add all the electoral votes together: \[180 + 72 + 39 + 12 = 303\]
• For each candidate, divide their received votes by the total votes. This gives a fraction representing their share of the total.
  
  For example, Abraham Lincoln received:\[\frac{180}{303} = 0.5941\]
• To convert this fraction to a percentage, multiply by 100:\[0.5941 \times 100 \approx 59.41\%\]

Repeating these operations for each candidate delivers a clear picture of their electoral success.

Historical Elections

The election of 1860 was a pivotal moment in American history. The nation was deeply divided, and the results of the election had long-lasting impacts.

A few key elements:

• Abraham Lincoln, representing the Republican Party, was primarily elected on a platform opposing the expansion of slavery.
• The division between Northern and Southern Democrats highlighted the regional tensions.
  J.C. Breckinridge and Stephen Douglas were symbolic of these divisions.
• The presence of the Constitutional Union Party, represented by John Bell, underscored the complexity of the political landscape.

This election's historical significance lies not only in its immediate aftermath—the American Civil War—but also in how it reshaped the political landscape for future generations.