A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets to the museum. Based on this information, how much is an adult ticket, and how much is a child ticket?
[tex]2a + 4c = 38.00[/tex]
[tex]3a + 3c = 40.50[/tex]
What values of [tex]a[/tex] and [tex]c[/tex] represent the solution to the system?
[tex]a = 8, c = 5.5[/tex]
What does the solution (8, 5.5) mean in the context of this problem?
A. The cost of 8 child tickets is $5.50.
B. The cost of 8 adult tickets is $5.50.
C. A child ticket costs $8, and an adult ticket costs $5.50.
D. An adult ticket costs $8, and a child ticket costs $5.50.
Answer (2)
The problem provides a system of equations representing the cost of adult and child tickets.
The solution (8, 5.5) is given, where 8 represents the value of 'a' (adult ticket cost) and 5.5 represents the value of 'c' (child ticket cost).
Therefore, an adult ticket costs $8 and a child ticket costs $5.50 .
The final answer is: $8 , $5.50 .
Explanation
Understanding the Problem We are given a system of two equations with two variables, a and c , representing the cost of an adult ticket and a child ticket, respectively. The equations are:
2 a + 4 c = 38.00 3 a + 3 c = 40.50
We are also given that the solution to this system is a = 8 and c = 5.5 . The question asks us to interpret what this solution means in the context of the problem.
Interpreting the Solution The variable a represents the cost of an adult ticket, and the variable c represents the cost of a child ticket. Therefore, the solution a = 8 means that the cost of an adult ticket is $8 , and the solution c = 5.5 means that the cost of a child ticket is $5.50 .
Final Answer Thus, the solution ( 8 , 5.5 ) means that an adult ticket costs $8 and a child ticket costs $5.50 .
Examples
Understanding systems of equations is crucial in various real-life scenarios. For instance, consider a bakery that sells cookies and cakes. If you know the total revenue from selling a certain number of cookies and cakes on two different days, you can set up a system of equations to find the price of a single cookie and a single cake. This helps in pricing strategies and inventory management.
The solution to the ticket pricing problem shows that an adult ticket costs $8, and a child ticket costs $5.50. Thus, the answer is option D. This interpretation follows from solving the given equations that represent the total costs of tickets for museum visits.
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