Answer:
The number of tickets and cookies for the school concert and reception can be solved using a system of linear equations. Let's call the number of tickets per student x. Since each student gets the same number of tickets, we can say that x is the same for all students.
We know that the total number of tickets is 72, so we can write the equation:
x + x + ... + x = 72
Since there are 72 tickets in total, we can write x = 72/n, where n is the number of students.
Now, let's look at the cookies. Since each student gets the same number of cookies as every other student, we can say that the number of cookies per student is the same as the number of tickets per student. So, we can use the same equation:
x + x + ... + x = 96
Since there are 96 cookies in total, we can write x = 96/n.
Now, we can solve for n, the number of students. We can do this by substituting one of the equations into the other. Let's use the equation for the tickets:
x + x + ... + x = 72
We can substitute x = 96/n, which gives us:
(96/n) + (96/n) + ... + (96/n) = 72
Now, we can simplify and solve for n:
n(96/n) = 72
n^2 = 72
n = 8
So, there are 8 students in total.
The number of tickets per student is 72/8 = 9, and the number of cookies per student is also 9.
Explanation: