Question

A movie theater sells tickets in two groups: Adults tickets (aged 18-65) which charge $5 Old or Young (over 65 or under 18 ) which are charged $3.25 One night there were 218 people that paid to see a movie and the theater took in $929. How many of each ticket group were sold?

Answer 1

To solve this problem, we can use a system of equations. Let's assume that the number of adult tickets sold is A, and the number of old or young tickets sold is OY. From the given information, we can set up a system of equations and solve them to find the values of A and OY. The solution is that 125 adult tickets and 93 old or young tickets were sold.

Step-by-step explanation:

To solve this problem, we can use a system of equations. Let's assume that the number of adult tickets sold is A, and the number of old or young tickets sold is OY.

From the problem, we know that the cost of an adult ticket is $5, and the cost of an old or young ticket is $3.25.

We also know that the total number of people who paid to see the movie was 218, and the total amount of money collected was $929.

From this information, we can set up the following equations:

1. A + OY = 218 (equation 1)
2. 5A + 3.25OY = 929 (equation 2)

Now we can solve the system of equations to find the values of A and OY.

Multiplying equation 1 by 3.25, we get:

• 3.25A + 3.25OY = 709.5 (equation 3)

Subtracting equation 3 from equation 2, we get:

• 5A - 3.25A = 929 - 709.5
• 1.75A = 219.5
• A = 219.5 / 1.75 = 125

Substituting the value of A into equation 1, we get:

• 125 + OY = 218
• OY = 218 - 125
• OY = 93

Therefore, 125 adult tickets and 93 old or young tickets were sold.