Question

The price for movie tickets at a cinema is $4 for children and $10 for adults. On Friday of last week, 1000 people attended a screening of the latest shoot-em- up blockbuster and $7000 is collected from tickets. How many children and how many adults bought tickets for the movie?

Answer 1

500 children and 500 adults bought tickets for the movie.

Step-by-step explanation:

To solve this problem, let's assume that x represents the number of children and y represents the number of adults who bought tickets for the movie. We can create a system of equations based on the given information:

1. x + y = 1000 (equation 1, because the total number of people who attended the screening was 1000)
2. 4x + 10y = 7000 (equation 2, because the total amount collected from ticket sales was $7000)

We can solve this system of equations by substitution or elimination method. Let's use the elimination method:

1. Multiply equation 1 by 4: 4x + 4y = 4000
2. Subtract equation 2 from the modified equation 1: (4x + 4y) - (4x + 10y) = 4000 - 7000
3. -6y = -3000
4. Divide both sides by -6: y = 500 (number of adults)
5. Substitute the value of y into equation 1: x + 500 = 1000
6. x = 500 (number of children)

Therefore, 500 children and 500 adults bought tickets for the movie.