City of Fun, an amusement park, charges $25 per child and $45 per adult. On an average summer day, they sell a total of 2,210 tickets and make $75,450. Based on this data, how many of each ticket type do they sell on an average summer day?
Answer (1)
Define variables: Let c be the number of child tickets and a be the number of adult tickets.
Set up equations: c + a = 2210 and 25 c + 45 a = 75450 .
Solve for a using substitution: a = 1010 .
Solve for c : c = 1200 . The number of child and adult tickets sold are 1200 and 1010 , respectively.
Explanation
Problem Analysis Let's analyze the problem. We are given the price of child and adult tickets, the total number of tickets sold, and the total revenue. We need to find the number of child and adult tickets sold.
Define Variables Let's define our variables:
Let c be the number of child tickets sold.
Let a be the number of adult tickets sold.
Set Up Equations We can set up a system of two linear equations based on the given information:
Equation 1 (total tickets): c + a = 2210
Equation 2 (total revenue): 25 c + 45 a = 75450
Solve for c in Equation 1 Now, let's solve the system of equations. We can solve the first equation for c :
c = 2210 − a
Substitute into Equation 2 Substitute this expression for c into the second equation:
25 ( 2210 − a ) + 45 a = 75450
Simplify the Equation Expand and simplify the equation:
55250 − 25 a + 45 a = 75450
20 a = 75450 − 55250
20 a = 20200
Solve for a Solve for a :
a = 20 20200
a = 1010
Solve for c Now that we have the number of adult tickets, we can find the number of child tickets using the equation c = 2210 − a :
c = 2210 − 1010
c = 1200
Conclusion So, there were 1200 child tickets and 1010 adult tickets sold on an average summer day.
Examples
Understanding ticket sales in amusement parks isn't just about numbers; it's about resource allocation and strategic planning. For instance, knowing the ratio of child to adult tickets helps in staffing decisions, optimizing ride queues, and tailoring marketing efforts. If an amusement park knows they sell significantly more child tickets, they might invest more in kid-friendly rides or family packages, enhancing customer experience and boosting revenue.
