Question 327857
For this problem we will identify the number of adult and student tickets.
We will assign the following variables:

Let x = number of adult tickets sold.
Let y = number of student tickets sold.

Here we can develop the following equations:

6x + 4.50y = 1395 (this equations tells us the amount of sales in dollars)
 x + y = 270 (this equation tells us the total units sold)

We can apply the elimination method used in a system of equations.

6x + 4.50y = 1395 (Equation 1)
x + y = 270 (Equation 2)

Lets multiply equation 2 by (-6) to eliminate x, thus solving for y.

We arrive at:

6x + 4.50y = 1395
-6x - 6y = -1620
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    -1.50 y = -225

Divide both sides by -1.50. Yielding:
y = 150

Next take y(150) and plug into equation 2 to solve for x.

x + 150 = 270
x = 120

Check your solutions:

120 + 150 = 270 Yes!!