Question

A child's ticket to the movie theater costs $9.95, and an adult ticket to the movie costs $12.95. A group of 10 people paid $105.50 to enter the movie. How many children and adults are in the group?

A. 4 children, 6 adults
B. 5 children, 5 adults
C. 6 children, 4 adults
D. 7 children, 3 adults

Answer 1

In a group of 10 people who paid a total of $105.50 to enter a movie, there are 8 children and 2 adults.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's say x represents the number of children and y represents the number of adults. The cost of x children's tickets is 9.95x and the cost of y adults' tickets is 12.95y. We can write two equations based on the given information:

1. x + y = 10 (because there are a total of 10 people in the group)

2. 9.95x + 12.95y = 105.50 (because the total cost of the tickets is $105.50)

Simplifying the first equation, we have x = 10 - y. Substituting this value into the second equation, we get:

9.95(10 - y) + 12.95y = 105.50

99.5 - 9.95y + 12.95y = 105.50

3y = 6

y = 2

Substituting y = 2 into the first equation, we get x = 10 - 2 = 8. Therefore, there are 8 children and 2 adults in the group.