algebra word problem.

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.

 

The Question:

Let x represent the number of the 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

Answer 1

Let x=members and y=non-members. Because there are 2 unknowns, 2 equations involving the unknowns must be found to solve the problem.

 Because the total number of students consists of members and non-members, x+y=19, or y=19-x (which is an answer to the original question). Also, 11x=cost of member tickets and 13y= cost of non-member tickets and 11x+13y=209.

 

 The 2 equations to solve this are:

                                                    y=19-x

                                                    11x+13y=209

Substituting: 11x+13(19-x)=209

Solving: 11x+247-13x=209

             11x-13x=209-247

                 -2x=-38

divide both sides by -2

                  x=19

Therefore, all students are members of the frequent visitor program.

 

    

Answer 2

x = number of students who are members.

 

both groups went together to the planetarium, and numbered 19.

This means 19-x is the number of people who are not members.

 

x number of people paid $11 for tickets and (19-x) number of people paid $13.

$11x+$13(19-x)=$209 for the total cost of the tickets.

 

If all 19 were not members, they would cost $13x19=$247

This means everybody who is an x would take away a $13, but be worth $11. 

 

$11x+ $247-$13x=$209

 

Solve for x and you know how many people are not members.

Answer 3

Let y represent the number of students in the group who are not members.

 

You can write an expression for y in terms of x from the information given.

 

What do you know?

 

The total number of students = 19

 

x + y = 19

 

which gives you

 

y = 19 - x

 

OR

 

you also know the total cost is 209 and you can use that and the cost of the two types of tickets to obtain an expression for y in terms of x.