First, it says to define our variables. When defining variables, you want to choose easy to remember variable names. For the sake of this problem, let's use s to represent the number of senior tickets and r to represent the number of regular tickets.
Second, it says to write out a system of equations. We have two totals given here, the total number of tickets sold and the total revenue from the tickets. So that means two equations. We know that there were 850 total tickets sold and there were only senior and regular tickets, so s + r = 850. We know the revenue (1650) and cost of the tickets for seniors and regulars (1.50 and 2.00, respectively), so we know that 1.5s + 2r = 1650.
Finally, it says to solve this system of equations by any method of your choosing. I'm going to do this by elimination since that is the method that is easiest for me. I'm going to eliminate r and isolate s. To do that, I'm gonna multiply the first equation by -2 and add it to the second equation. In this case -2(s+r) = -2*850 implies -2s-2r = -1700. By adding that to the second equation we get -2s-2r+1.5s +2r = -1700+1650 which, after cancelling out, means that -0.5s = -50, which implies s = 100. Since we know s = 100, we can substitute that into either of our equations to get r. The first one seems to be a tad easier, so we'll do that one. Since s+r = 850 and s = 100, 100+ r = 850, which means r = 750.
To sum up, there were 100 seniors tickets sold and 750 regular tickets sold.
