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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?

 Aug 5, 2020
 #1
avatar+21953 
+1

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.

 Aug 5, 2020
 #2
avatar+169 
+2

Latexified::

\(10.50A + 3.75(250 - A) = 2071.50\\ \Rightarrow10.50A + 937.50 - 3.75A = 2071.50\\ \Rightarrow6.75A + 937.50 = 2071.50\\ \Rightarrow6.75A = 1134.00\\ \Rightarrow A = 168\\\)

Inspirational  Aug 6, 2020

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