Question

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!​

Answer 1

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:

$\left \{ {{42o+25m=486} \atop {o+m=14}} \right.$

You can apply the Substittution Method to solve the system of equations:

1. Solve for "o" from the second equation:

$o=14-m$

2. Substitute it into the first equation and solve for "m":

$42(14-m)+25m=486\\\\588-42m+25m=486\\\\-17m=-102\\\\m=\frac{-102}{-17}\\\\m=6$

3. Substitute the value of "m" into $o=14-m$ and evaluate, in order to find the value of "o". This is:

$o=14-6\\\\o=8$