It costs $24 for two adults and two children to see a movie, and it costs the same amount for one adult and four children to see the same movie. Which statement is true?
It costs $24
for two adults and two children to see a movie, and it costs the same amount for one adult and four children to see the same movie. Which statement is true?
The statement "2 adults and 2 children can see the movie for the same price as 1 adult and 4 children" is true, and can be represented by the system of equations:
2a + 2c = 24
a + 4c = 24
where a is the cost for one adult and c is the cost for one child.
Well, it looks like we've got a mathematical riddle here! Let's see if we can solve it with a pinch of humor.
According to the information provided, we have two scenarios:
1) Two adults and two children: $24
2) One adult and four children: $24
Now we need to determine which statement is true.
Considering the ticket prices, we can conclude that children are getting a better deal than adults. I guess it's payback for having to eat all those vegetables!
But to answer the question, the true statement is: "Kids always know how to score the best discounts on movie tickets!"
To solve this problem, let's assign variables to the number of adults and children. Let's say 'a' represents the number of adults and 'c' represents the number of children.
According to the given information, the cost for two adults and two children is $24. This can be expressed as:
2a + 2c = $24
Similarly, the cost for one adult and four children is also $24. So we have:
1a + 4c = $24
Now we need to determine which statement is true based on these equations.
Statement 1: There is a direct relationship between the number of adults and the number of children.
This statement suggests that if we increase the number of adults, the number of children will also increase proportionally, and vice versa. To verify this, we can compare the coefficients of 'a' and 'c' in both equations.
Coefficient of 'a' in the first equation = 2
Coefficient of 'a' in the second equation = 1
Coefficient of 'c' in the first equation = 2
Coefficient of 'c' in the second equation = 4
Since the coefficients are not the same, this statement is NOT true.
Statement 2: Each child's ticket costs less than an adult's ticket.
This statement implies that the cost of an adult's ticket is higher than the cost of a child's ticket. To confirm this, we can analyze the given equations.
From the first equation, we can rewrite it as:
2a = $24 - 2c
From the second equation, we can rewrite it as:
a = $24 - 4c
Now we can compare the coefficients of 'a' in both equations.
Coefficient of 'a' in the first equation = 2
Coefficient of 'a' in the second equation = 1
Since the coefficient of 'a' in the first equation (for two adults and two children) is greater than the coefficient of 'a' in the second equation (for one adult and four children), it means the cost of an adult's ticket is higher than the cost of a child's ticket. Therefore, this statement is TRUE.
To summarize, the correct statement is: Each child's ticket costs less than an adult's ticket.
2a+2c = 24
a+4c = 24