SOLUTION: A group of 19 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetariums frequent visitor program & $13 for each studen

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A group of 19 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetariums frequent visitor program & $13 for each studen      Log On


   

Question 902920: A group of 19 students want to see the show at the planetarium. Tickets cost $11 for each student who is a member of the planetariums frequent visitor program & $13 for each student who is not a member. The total cost of the students tickets is $209.
1. Write an equation to determine the value of x. Explain what each part of your equation represents.
Found 2 solutions by josgarithmetic, richwmiller:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
u = students on the frequent visitor program
v = regular students at full price

highlight%28system%28u%2Bv=19%2C11u%2B13v=209%29%29

Note that 209%2F11=19, so this may help to know.

...the system as system%2811u%2B11v=209%2C11u%2B13v=209%29 shows something is wrong with the given information.
11u+11v should NOT equal 11u+13v.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
m+n=19,
11*m+13*n=209
m=19-n
11*(19-n)+13*n=209
209-11n+13*n=209
2*n=0
n=0
m=19-n
m=19 at $11 and n=0 at $13
check
19+0=19
11*m+13*n=209
11*19+13*0=209
209+0=209
209=209
ok
This means that all students were members and paid $11