Question

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 planetarium's frequent visitor program and $13 for each student who is not a member. The total cost of the students' tickets is $209. Use this information for Items 9–16.

Answer 1

All the student are members of the planetarium's frequent visitor program.

Explanation:

Let x represent the number of student who are members of the planetarium's frequent visitor program.

And let y represent the who are not a member.

Then two equations can be formed using the provided data:

x + y = 19...(i)

11x + 13y = 209...(ii)

Multiply (i) by 13 and solve for x as follows:

13x + 13y = 247

-11x - 13y = -209

2x = 38

x = 19

Substitute x = 19 in (i) and solve for y as follows:

x + y = 19

19 + y = 19

y = 0

Thus, all the student are members of the planetarium's frequent visitor program.