Every attends at monster truck rally paid the same admission fee. How many people attended the rally?
(1) If the admission fee raised to $20 and twice as many pepole had attended, the total admission fees collected would have been three times greater.

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = the number of people who attended the rally.
- \( y \) = the admission fee per person.

### Step 2: Write the Original Revenue Equation
The total revenue collected from the rally can be expressed as:
\[ \text{Original Revenue} = x \cdot y \]

### Step 3: Analyze the New Scenario
According to the problem, if the admission fee is raised to $20 and twice as many people attended, the new number of attendees would be \( 2x \) and the new admission fee is $20.

The new revenue can be expressed as:
\[ \text{New Revenue} = 2x \cdot 20 = 40x \]

### Step 4: Set Up the Equation Based on the Given Condition
The problem states that the new revenue is three times the original revenue. Therefore, we can set up the equation:
\[ 40x = 3 \cdot (x \cdot y) \]

### Step 5: Simplify the Equation
Rearranging the equation gives:
\[ 40x = 3xy \]

### Step 6: Solve for \( y \)
To isolate \( y \), we can divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[ 40 = 3y \]
\[ y = \frac{40}{3} \]

### Step 7: Conclusion
Now we have found the value of \( y \) (the admission fee per person) as \( \frac{40}{3} \) dollars. However, we still need to find the number of attendees \( x \).

Since we have the relationship \( 40x = 3xy \), we can substitute \( y \) back into this equation to find \( x \):
\[ 40x = 3x \cdot \frac{40}{3} \]
This simplifies to:
\[ 40x = 40x \]
This is a tautology, indicating that there are infinitely many solutions for \( x \) depending on the admission fee \( y \).

### Final Answer
Since we don't have enough information to determine a unique value for \( x \), we conclude that the data is insufficient to find the exact number of attendees.

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