I need help solving this algebra question. Can someone help? Thank you!

Question

Mr. Frankel bought 5 tickets to a puppet show and spent $22. He bought a combination of child tickets for $2 each and adult tickets for $8 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought? 

Answer 1

First, let us determine the system of equations that will lead to the solution.

The relationship described above can be rewritten as $2 x c tickets + $8 x a tickets = $22, the amount Mr. Frankel spent. Put even more simply, 2c + 8a = 22. We also know that the total number of tickets (c tickets + a tickets) is 5, therefore c + a = 5.

To determine the value of c and a respectively, we must choose one and combine the two equations to eliminate the other variable. Let us start with c.

We can easily solve the second, simpler, equation for a, the variable we want to eliminate: a = 5 - c. We then substitute (5 - c) for a in our more complicated equation: 2c + 8(5 - c) = 22. If we simplify this... [2c + 40 - 8c = 22] becomes [40 - 6c = 22] which becomes [40 - 22 = 6c] which becomes [18 = 6c] so c = 3.

Using our simple c + a = 5 equation, we can then easily determine that a = 2.

Let me know if you need any further explanation!