Question

A group of 19 students want to see the show at the planetarium. The tickets cost $11 for each student who is a member of the planetariums frequent visitor program and $13 for each student who is not a member. The total cost of the students' tickets is $209.
Let x represent the number of students in the group who are members of the frequent visitor program. Write an expression in terms of x for the number of students in the group who are not members. Then write an equation to determine the value of x.

Answer 1

If the amount of members are y, then the total number of people who attend is x+y=19. In addition 11*y (since it costs 11 dollars per member)+13*x=209. Subtracting x from both sides in the first equation, we get y=19-x. Plugging that into the second equation, we get (19-x)*11+13*x=209. Multiplying it out, we get 201-11x+13x=209. Subtracting 201 from both sides, we get 2x=8 and by dividing both sides by 2 we get x=4