Two students fought a college election. The winning students got `60%` of the total votes and and won the election by 144 votes. What was the total number of votes polled?

Options

A. 720
B. 360
C. 480
D. 240

Answer

To solve the problem, we need to find the total number of votes polled in the election. Let's break it down step by step.

### Step 1: Define the total number of votes
Let the total number of votes be represented by \( x \).

### Step 2: Calculate the votes received by the winning student
According to the problem, the winning student received 60% of the total votes. Therefore, the votes received by the winning student can be calculated as:
\[ \text{Votes received by winning student} = 0.6x \]

### Step 3: Calculate the votes received by the losing student
Since there are only two students, the losing student received the remaining votes. The remaining votes can be calculated as:
\[ \text{Votes received by losing student} = x - 0.6x = 0.4x \]

### Step 4: Set up the equation based on the winning margin
According to the question, the winning student won by 144 votes. This means the difference between the votes received by the winning and losing students is 144. We can set up the equation as follows:
\[ 0.6x - 0.4x = 144 \]

### Step 5: Simplify the equation
Now, simplify the left side of the equation:
\[ 0.2x = 144 \]

### Step 6: Solve for \( x \)
To find the total number of votes \( x \), divide both sides of the equation by 0.2:
\[ x = \frac{144}{0.2} = 720 \]

### Conclusion
The total number of votes polled in the election is \( 720 \).

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