Question

The cost of a ticket to the circus is $11.00 for children and $36.00 for adults. On a certain day, attendance at the circus was 1,100 and the total gate revenue was $27,100. How many children and how many adults bought tickets?

Answer 1

To find the number of children and adults who bought tickets to the circus, we can set up a system of equations. Solving this system gives us 500 children and 600 adults.

Step-by-step explanation:

To solve this problem, we can set up a system of equations based on the information given. Let x represent the number of children and y represent the number of adults.

We know that the total attendance was 1,100, so we have the equation x + y = 1,100.

We also know that the total gate revenue was $27,100, so we have the equation 11x + 36y = 27,100.

Now we can solve this system of equations to find the values of x and y. Multiplying the first equation by 11 gives us 11x + 11y = 12,100. Subtracting this equation from the second equation, we get 36y - 11y = 27,100 - 12,100. Simplifying, we have 25y = 15,000. Dividing both sides by 25, we find y = 600. Substituting this value back into the first equation, we can find x: x + 600 = 1,100, so x = 500.

Therefore, 500 children and 600 adults bought tickets to the circus.