Linear function

Question

A local theater sells tickets for childre, adults, and senior citizen. Adult tickets are $8.00, children's tickets are $4.00, and senior tickets are $6.00. One day the theater sells 700 tickets and makes $4580.00. The sum of the number of children's tickets sold and twic the amount of senior tickets sold is 50 less than the amount of adult tickets sold. How many of each tickets are sold?

Answer 1

Ok to do this you need to set some basic ground rules. First, given your information, this is a systems of equations question so your first step is to do the basic setup.

 

First assign a variable for each type of ticket.

Let's say:

A = Children's Tickets Sold

B = Adult Tickets Sold

C = Senior Tickets Sold

 

We know that total sales amount to 700, so

A + B + C = 700

 

We know that Children's Tickets and double the Senior Tickets combine to less than 50 adult tickets. Therefore:

A+ 2C = B - 50 or B = A+2C+50

 

We can also use the dollar amount made to form an equation based on the total revenue by multiplying the dollar value made off of each ticket by the amount that each ticket sold for to get total revenue:

4A + 8B + 6C =4580

 

At this point, you want to use your three equations to convert everything into one type of ticket.

 

Once you find the value for one of the tickets, substitute that number in for each of the equations to find total tickets sold for each variable; A, B and C!

 

Hope this helps!