The Smith family went to the theater to see a movie. Adult ticket cost $12 and child tickets cost $9. If they spent $75 total and purchased 7 tickets. How many of each were purchased?

Question

Adult-9

Children-4

Answer 1

For this problem we will want to set up a system of equations. Let's assume x=number of adult tickets and y=number of children tickets.

The first equation is x+y=7 as the Smith family purchased a total of 7 tickets.

The second equation is 12x+9y=75 as the number of tickets multiplied by the price gets you the amount spent on the tickets and if you add the amount spent on adult and child tickets you will get the total spent, which in this case is $75.

From here we can solve this system of equations by elimination or substitution, but I will use elimination. To use elimination we need to get rid of one of the variables like this

12(x+y)=7

12x+12y=84

12x+9y=75

We can now subtract these two equations to get, because the x cancels each other out.

3y=9

Therefore y=3, we can now plug this into the original equation x+y=7 to solve for x.

x+3=7, x=4.

We will want to plug these values into the other equation to ensure it works.

12(4)+9(3)=75

48+27=75

75=75

Therefore the Smith family purchased 4 adult tickets and 3 children's tickets.