is the answer correct?
Alice’s school is selling tickets to the school carnival. On the first day of ticket sales, the school sold 3 adult tickets and 9 student tickets for a total of $75. The second day, the school sold $67 by selling 8 adult and 5 student tickets. What is the price each of one adult and one student ticket?
answer: student price $7, adult price $4
Haha, good.
To determine if the answer provided is correct, let's check if it satisfies both given conditions.
Condition 1: On the first day, the school sold 3 adult tickets and 9 student tickets for a total of $75.
Let's calculate the cost of the tickets on the first day using the provided prices:
3 adult tickets at $4 each = 3 * $4 = $12
9 student tickets at $7 each = 9 * $7 = $63
Thus, the total cost of the tickets on the first day is $12 + $63 = $75. This matches the given information, so the first condition is satisfied.
Condition 2: On the second day, the school sold $67 by selling 8 adult and 5 student tickets.
Let's calculate the cost of the tickets on the second day using the provided prices:
8 adult tickets at $4 each = 8 * $4 = $32
5 student tickets at $7 each = 5 * $7 = $35
Thus, the total cost of the tickets on the second day is $32 + $35 = $67. This also matches the given information, so the second condition is satisfied.
Since both conditions are met, we can conclude that the answer provided is correct. One adult ticket costs $4, and one student ticket costs $7.
To find the price of one adult ticket and one student ticket, we can set up a system of equations based on the information given.
Let's assume that the price of one adult ticket is 'a' dollars, and the price of one student ticket is 's' dollars.
From the first day of ticket sales, we know that 3 adult tickets and 9 student tickets were sold, resulting in a total revenue of $75. Therefore, we can write the equation:
3a + 9s = 75 ----(1)
Similarly, from the second day of ticket sales, we know that 8 adult tickets and 5 student tickets were sold, resulting in a total revenue of $67. This gives us the second equation:
8a + 5s = 67 ----(2)
Now we have a system of two equations with two variables (a and s). We can solve this system of equations to find the values of 'a' and 's'.
First, let's solve the system through the substitution method:
From equation (1), we can solve for 'a' in terms of 's':
3a = 75 - 9s
a = (75 - 9s)/3
a = 25 - 3s ----(3)
Now, substitute the value of 'a' from equation (3) into equation (2):
8(25 - 3s) + 5s = 67
200 - 24s + 5s = 67
-19s = -133
s = 7
Substitute the value of 's' back into equation (3) to find 'a':
a = 25 - 3(7)
a = 25 - 21
a = 4
Therefore, the price of one adult ticket is $4, and the price of one student ticket is $7.
3a+9s = 75
8a+5s = 67
The answer is correct, but what a ripoff!
What school charges more for student tickets than for visitors?