For a production of sweeney todd in las vegas, orchestra seats cost $42 and mezzanine seats cost $25. if a group of 14 people show up and spend a total of $486, how many of each kind of seat did they buy? please help, please show work!
Accepted Solution
A:
Answer: 8 orchestra seats and 6 mezzanine seats.Step-by-step explanation: Let be "o" the number of orchestra seats they bought and "m" the number of mezzanine seats they bought. Set up a system of equations: [tex]\left \{ {{42o+25m=486} \atop {o+m=14}} \right.[/tex] You can apply the Substittution Method to solve the system of equations: 1. Solve for "o" from the second equation: [tex]o=14-m[/tex] 2. Substitute it into the first equation and solve for "m": [tex]42(14-m)+25m=486\\\\588-42m+25m=486\\\\-17m=-102\\\\m=\frac{-102}{-17}\\\\m=6[/tex] 3. Substitute the value of "m" into [tex]o=14-m[/tex] and evaluate, in order to find the value of "o". This is: [tex]o=14-6\\\\o=8[/tex]