Question

2. 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 tha) can be used to determine the
number of adult and student tickets purchased.
b. Determine the number of adults tickets sold and the number of
student tickets sold. Use mathematics to explain how you
determined your answer.

Answer 1

a = 950

s = 550

Explanation:

Let a = the number of adult tickets purchased.

Let s = the number of student tickets purchased.

Therefore,

`a + s = 1500 \implies \: s = 1500 - a...(1) \\ 2a + 3.5s = 3825...(2) \\ plugging \: s = 1500 - a \: in \: equation \: (2) \\ 2a + 3.5(1500 - a) = 3825 \\ 2a + 5250 - 3.5a = 3825 \\ 5250 - 1.5a = 3825 \\ 5250 - 3825 = 1.5a \\ 1425 = 1.5a \\ a = (1425)/(1.5) \\ \huge \red{ \boxed{ a = 950}} \\\implies s = 1500 - 950 \\ \huge \purple{ \boxed{s = 550}}`

So,

Number of adult tickets sold = 950

Number of students tickets sold = 550