Jillian’s school is selling tickets for a play. The tickets cost $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. If a total of 250 people attended, how many were adults and how many were students?
+23252 Let A = number of adult tickets sold and S = number of student tickets sold.
Number of tickets sold equation: A + S = 250
Value of tickets sold equation: 10.50A + 3.75S = 2071.50.
Solving the first equation for S: S = 250 - A.
Substituting this into the second equation: 10.50A + 3.75(250 - A) = 2071.50
---> 10.50A + 937.50 - 3.75A = 2071.50
---> 6.75A + 937.50 = 2071.50
---> 6.75A = 1134.00
---> A = 168
Knowing the value of A, you can now find the value of S.
+169 Latexified::
\(10.50A + 3.75(250 - A) = 2071.50\\ \Rightarrow10.50A + 937.50 - 3.75A = 2071.50\\ \Rightarrow6.75A + 937.50 = 2071.50\\ \Rightarrow6.75A = 1134.00\\ \Rightarrow A = 168\\\)
