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]
