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# System of equations

You are selling tickets for a high school concert. Student tickets cost four dollars dollars and general admission tickets cost six dollars. You sell 450 tickets and collect \$2340. How many of each type of ticket did you sell?

Another way, using Simultaneous Equations:

Numbers of tickets: Student (s) tickets + General Admission (g) tickets = 450, or s + g = 450

Numbers of dollars: 4s + 6g = 2340

4s + 6g = 2340

s + g = 450. Multiply the bottom equation by -4: -4s - 4g = -1800

Now we have:

4s + 6g = 2340

-4s - 4g = -1800

+2g = 540

or g = 270, the number of General Admissions tickets sold

s + g = 450; s = 450 - g; s = 450 - 270, so s = 180, the number of Student tickets sold

Check the dollar amounts:

4s + 6g = 2340

4(180) + 6(270) = 2340; 720 + 1620 = 2340, and 2340 = 2340, so we know we are correct.

Two things you need to consider:
the quantity of tickets sold and the number of each ticket times the price of each ticket.

That give us
x = student tickets

We know that
x + y = 450 tickets
4x + 6y = \$2340

Now, solve the first equation for y to get
y = 450 - x

and plug it in to the second equation
4x + 6(450 - x) = 2340

Simplify and solve for x. This gives you the number of student tickets sold.

Then, plug this value into the first equation and solve for y.

These last few steps have been left for the student.