Michael J. answered • 06/08/15

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Assign variables for the number of each kind of ticket, since this is what we want to find out.

Let the number of student tickets = x

Let the number of adult tickets = y

Now, we write equations that describes the situation.

x + y = 56 defines the total tickets.

3.5x + 4.5y = 215 defines the total price.

These are the equations we will work with.

x + y = 56 eq1

3.5x + 4.5y = 215 eq2

We have a system of equations. Let's substitute eq1 into eq2, so that we have only equation with one variable.

3.5x + 4.5(56 - x) = 215

Solve for x.

3.5x + 252 - 4.5x = 215

-x + 252 = 215

-x = -37

x = 37

Substitute this value of x into eq1 to solve for y.

y = 56 - x

y = 56 - 37

y = 19

She sold 37 student tickets and 19 adult tickets.