Question

In a circus company the price of tickets for adult and children were 50 and 30 respectively. The company has sold a total of 1000 tickets. The average (arithmetic mean) price per ticket sold was 42. How many tickets were sold for children?

• A. 200
• B. 300
• C. 400
• D. 600
• E. 800

Hint:

To solve average-related problems, set up an equation using the formula for average: \[ \text{Average} = \frac{\text{Total sum}}{\text{Number of items}} \]

Answer 1

The Correct Option is C

Step 1: Use the average price formula.
We are given that the total number of tickets sold is 1000, and the average price of the ticket sold is \$42. The price of adult tickets is \$50, and the price of children’s tickets is \$30.
Let the number of children’s tickets sold be \( x \), and the number of adult tickets sold be \( 1000 - x \).
Step 2: Set up the equation for the average price.
The total price of tickets sold is the sum of the prices of adult and children’s tickets: \[ 50(1000 - x) + 30x = 42 \times 1000 \] Step 3: Simplify the equation.
\[ 50(1000 - x) + 30x = 42000 \] \[ 50000 - 50x + 30x = 42000 \] \[ 50000 - 20x = 42000 \] \[ -20x = 42000 - 50000 \] \[ -20x = -8000 \] \[ x = \frac{-8000}{-20} = 400 \] Step 4: Conclusion.
The number of children’s tickets sold is 400. So, the correct answer is (C) 400.