Question

there were 200 tickets sold for a college basketball game. Tickets were $4.50 for students and $9 for adults. The total amount collected was $1485. How many of each type of ticket were sold

Answer 1

`70` tickets were sold to student and
`130` tickets were sold to adults

Step-by-step explanation:

Let the number of tickets purchased by students be "X" and the number of tickets purchased by adults be "Y"

Given

Total number of tickets sold
`= 200`

Total amount collected by selling
`200` tickets
`= 1485` dollar

Cost of one ticket of student
`= 4.5` dollar

Cost of one ticket of adult
`=` 9 dollar

Two equation are as follows

`X + Y = 200\\` ------Eq (1)

`4.5 X + 9 Y =1485` -------- Eq (2)

Multiplying eq (1) by 9 and subtracting from equation 2 we get

`4.5 X - 9 X + 9Y -9Y = 1485 - (200* 9)\\-4.5 X = -315\\X = 70`

Substituting the value of X in equation 1 we get

`70 + Y = 200\\Y = 200 -70 \\Y = 130`

Therefore,
`70` tickets were sold to student and
`130` tickets were sold to adults