The symphony sells two kinds of tickets: orchestra, for $40, and upper

O + U = 90

45O * 25U = 2625

Two equations, two variables, solving will give O = 25

Hence, Answer is A

MAGOOSH OFFICIAL SOLUTION:

Notice, in verbal form, this is a two-equations-two variables problem. The two variables are x = the number of orchestra tickets, and y = the number of upper tier tickets.

One equation we get is x + y = 90, for the total number of tickets sold. That’s one equation. If we sell x orchestra tickets, we get $40 for each, so we get 40x in total revenue from all of the orchestra tickets. Similarly, we get 25y in total revenue from all the upper tier tickets. Thus, the total revenue is 40x + 25y = 2625. That’s our second equation.

The first equation is incredibly convenient to multiply. I would rather multiply by 40 than by 25, so I make the coefficients of x match. I’ll multiply the first equation by 40, and the second equation by –1.

40x + 40y = 3600
(-40x - 25y = 2625)
_______________
15y = 975

Now, at first blush, that might look like an ugly division problem awaiting us, 975 divided by 15. Let’s break it down a bit. I know 900/3 = 300, and 75/3 = 25, so if I divide both sides by 3, I get

5y = 975/3 = 325

Now, 100/5 = 20, so three times that is 300/5 = 60. Of course, 25/5 = 5, so

y = 325/5 = 65

We want x, so x + (65) = 90 right x = 25, answer = A.

BTW, if these steps totally elude you, remember you can always backsolve from the numerical answers as a backup strategy.

We are given that A + B = 90 (A and B representing both ticket types), and that 40A + 25B = 2625. You may factor out 5 from the latter equation just to make the numbers easier to work with. It becomes 8A + 5B = 525.
Since A + B = 90, then B= 90 - A. We are solving for A so it is easier to write the equation in terms of A.
8A + 5 (90-A) =525
8A + 450 - 5A= 525
3A=75
A=25

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