There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?
• Let a = the number of adult tickets purchased.
• Let s = the number of student tickets purchased.
a. Write a system of equations that can be used to determine the number of adult and student

Question

There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets? 
•	Let a = the number of adult tickets purchased.
•	Let s = the number of student tickets purchased.
a.	Write a system of equations that can be used to determine the number of adult and student

andrewhaze · Answer

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anonymous · Answer

let a be the number of adult ticket and s the number of children:
We have the first equation is: a +s = 1500 (the number of adult plus children tickets)
And for the second equation, we have: (3.50)a + (2)c=3825
From this point, there are several ways to solve this system, but it this case, let's do the elimination method (aka addition method)
a+s=1500
3.50a+ 2s =3825 (We'll need to find the number that when multiply that number to either the first or second equation, one of the equation will cancel out and in this case, (-2))
so far, we have:
(a+s=1500) x (-2)
3.50a +2s=3825

-2a -2s= -3000
3.50a+2s=3825
Now, add the two equations together, we'll have
1.5a= 825 ---->Solve for a, we'll have
a=550----> Adult:550
But we're not quite done yet, we have to go back to either one of the equation and plug in the value for a (which is 550) and solve  for the number of students
a+s=1500
(550)+s=1500
s=950
The answer is, I believe, 950 students bought the tickets.