Question

During a presidential election, a high school held its own mock election. Students had the option to vote for Candidate A, Candidate B, or several other candidates. They could also choose to spoil their ballot. The table below displays a summary of the election results. $$ \begin{array}{|l|c|c|c|c|} & \text { Candidate A } & \text { Candidate B } & \text { Other } & \text { Total } \\ \hline \text { 10th grade } & 0.32 & 0.58 & 0.10 & 1.00 \\ \hline \text { 11th grade } & 0.50 & 0.42 & 0.08 & 1.00 \\ \hline \text { 12th grade } & 0.63 & 0.32 & 0.05 & 1.00 \\ \hline \text { Total } & 0.48 & 0.44 & 0.08 & 1.00 \\ \hline \end{array} $$ 614 students voted for Candidate A. Approximately how many students attend the school?

Short answer

Approximately 1279 students attend the high school.

Step-by-step solution

Identify the percentage of students who voted for Candidate A

From the table, we can see that 48% (0.48) of the total students voted for Candidate A.

Find the total number of students

We know that 614 students voted for Candidate A, and they represent 48% (0.48) of the total students. Let's call the total number of students "x". To find the total number of students (x), we need to set up the equation: \(0.48x = 614\)

Solve the equation

Now, to find the value of "x", we need to divide both sides of the equation by 0.48: \( x = \frac{614}{0.48} \)

Calculate the total number of students

Now, let's calculate the value of "x": \( x \approx \frac{614}{0.48} \approx 1279 \) So, approximately 1279 students attend the high school.

Key concepts

Mock Election

A mock election is a simulation of an actual election, often conducted in schools or educational settings. This gives students a hands-on experience in the democratic process. In the context of our high school exercise, students cast their votes for their preferred candidates—Candidate A, Candidate B, or other candidates—as well as the option to spoil their ballot.
Mock elections serve several educational purposes:

• They teach students about the electoral process and the importance of participating in democratic activities.
• They encourage engagement with current events and political issues.
• They help students develop critical thinking and analytical skills by evaluating different candidates and making informed decisions.

In the mock election, detailed results help students understand and analyze voting patterns. For example, they could investigate any disparities in candidate preference across different grade levels.

High School Math

High school math is crucial as it covers fundamental concepts that are used in real-life situations and further studies. In our given exercise, the focus is on percentage problems.
Understanding percentages and their application is a key part of high school math:

• Percentages represent a part out of a total. In this exercise, for instance, each candidate received a percentage of the total votes.
• It helps in understanding the distribution and comparison of data, such as how votes were spread among different candidates or how 48% of students voted for Candidate A.
• Developing skills to work with percentages equips students with the ability to tackle more complex problems in subjects like finance or data analysis later on.

By engaging with exercises like these, students get to reinforce their understanding of communicating mathematically and interpreting data effectively.

Equations Solving

Solving equations is a fundamental skill in algebra that high school students need to master. It enables them to find unknown values, much like the student population in our exercise. Here, we employed equation-solving strategies to determine how many students attended the school in total.
To solve an equation like \(0.48x = 614\), these are the steps:

• Identify the known and unknown quantities: 0.48 or 48% represents the portion of students who voted for Candidate A, and 614 is the actual count of those voters.
• Set up the equation: Here the mathematical relationship between the total number of students and those who voted for Candidate A is expressed as \(0.48x = 614\).
• Solve for the unknown: This involves rearranging the equation to isolate \(x\) by performing operations like division, resulting in \(x = \frac{614}{0.48}\).
• Calculate the result: Solving the equation tells us that the approximate total number of students is 1279.

This approach not only helps find specific numerical answers but also builds logical reasoning and problem-solving skills.