Bunuel
A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 350 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
(A) 90
(B) 110
(C) 120
(D) 130
(E) 220
Kudos for a correct solution.
KAPLAN OFFICIAL SOLUTION:The first step in this problem is to translate our word problem into math. We can write two equations based on the information in the question stem. If we call balcony seats B and orchestra seats R (we want to avoid using the letter O as a variable because it looks like the number 0), we can write one equation based on the number of seats sold and one equation based on the amount of money made. These equations are:
R + B = 350
12R + 8B = 3,320
Next, we need to combine these equations to solve for one of the variables. We can rewrite R + B = 350 as B = 350 – R and substitute (350 – B) in for R in our other equation. This gives us 12R + 8(350 – R) = 3,320. From here, we can solve for R as follows:
12R + 8(350 – R) = 3,320
12R + 2800 – 8R = 3,320
4R = 520
R = 130
Next we plug 130 in for R in our initial equation and solve for B:
130 + B = 350
B = 220
Finally, we need to find out how many more balcony seats than orchestra seats we have by subtracting the two results. This gives us 220 – 130 = 90, which is
answer choice (A).