i need help setting this problem up to solve.

Question

Last spring, several of the mhcc jazz groups held a joint concert. Tickets sold for $8 to the general public and $5.50 for students and staff. Ticket sales brought in $2582.50. If 390 people attended the concert, how many were students and staff and how many were general public?

Answer 1

Lets use some variables

g=general public

s=student and staff

 

Now let's translate each section into an equation:

Tickets sold for $8 to the general public and $5.50 for students and staff. Ticket sales brought in $2582.50.

  8g+5.5s=2582.50

 

390 people attended the concert -> that means general public and students&staff

  g+s=390

 

Solve by substitution:

We can only solve for one variable at a time.  Here's how we get it down to one.

 isolate g by subtracting s from both sides of g+s=390

                                                                   -s    -s

                                                                  g=390-s

 

Now substitute g in 8g+5.5s=2582.50

8(390-s)+5.5s=2582.50   now we only have 1 variable, s

 

solve for s.  Be careful with distribution and combining like terms.

 

when you have s, substitute that number in for s in the equation g+s=390 and solve for g.