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.

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=(-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`