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?
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?
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To solve average-related problems, set up an equation using the formula for average:
\[
\text{Average} = \frac{\text{Total sum}}{\text{Number of items}}
\]
Updated On: Oct 3, 2025
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The Correct Option is C
Solution and Explanation
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.
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.
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