Every attends at monster truck rally paid the same admission fee. How many people attended the rally?
(2) If the admission fee had been raised to $30 and two-thirds as may people had attended, the total admission fees collected would have been 150% of the actual admission fees collected

Answer

To solve the problem step by step, we can follow these steps:

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

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

### Step 3: New Conditions
According to the problem:
- The admission fee is raised to $30.
- The number of attendees becomes two-thirds of the original number of attendees, which is \(\frac{2}{3}x\).

### Step 4: Calculate New Revenue
The new revenue can be calculated as:
\[ \text{New Revenue} = \left(\frac{2}{3}x\right) \cdot 30 \]
This simplifies to:
\[ \text{New Revenue} = 20x \]

### Step 5: Set Up the Equation for Revenue Increase
It is given that the new revenue is 150% of the original revenue. We can express this mathematically as:
\[ 20x = 1.5 \cdot (x \cdot y) \]
This can also be written as:
\[ 20x = \frac{150}{100} \cdot (x \cdot y) = \frac{3}{2} \cdot (x \cdot y) \]

### Step 6: Simplify the Equation
Now, we can simplify the equation:
\[ 20x = \frac{3}{2}xy \]
To eliminate \( x \) from both sides (assuming \( x \neq 0 \)), we can divide both sides by \( x \):
\[ 20 = \frac{3}{2}y \]

### Step 7: Solve for \( y \)
To find \( y \), we can multiply both sides by \( \frac{2}{3} \):
\[ y = \frac{20 \cdot 2}{3} = \frac{40}{3} \approx 13.33 \]

### Step 8: Conclusion
Now we have the admission fee \( y \approx 13.33 \). However, we still need to find \( x \). Since we have only one equation and two unknowns, we cannot determine the exact value of \( x \) without additional information.

Thus, the conclusion is that the data is insufficient to determine the exact number of attendees at the rally.

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