For the Event to Kings Island the cost for an adult ticket is $20 and the cost for a student ticket is $10. The tickets are purchased in advance and a total of 550 tickets were purchased and the total cost of the tickets was $7,500.

Identify the total number of adult tickets and student tickets sold that would create a total of 550 tickets sold for a total cost of $7,500.

We have two formulas:

Adult tickets plus Student tickets = 550 tickets or A + S = 550

and

Adult tickets times $20 plus Student ticket times $10 = $7500 or

(A * 20) + (S * 10) = 7500

First let's get rid of one of the variables by re-balancing the simplest formula

A+S = 550

A+S-A = 550-A

S = 550-A

Now we can restate the second formula replacing "S" with it's equivalent "550-A"

(A * 20) + (S * 10) = 7500

(A * 20) + ((550-A) * 10) = 7500

Then do the multiplication

20A + 5500 - 10A = 7500

and simplifiy

20A + 5500 - 5500 - 10A = 7500 - 5500

20A - 10A = 2000

10A = 2000

A = 200

S = 550 - 200 = 350

Now we should test the answers to be sure our work

is correct:

200 Adult tickets times $20 = $4000

350 Student tickets times $10 = $3500

$4000 + $3500 = 7500