Writing a Two-Variable Equation to Model a Scenario

Tickets at a movie theater cost $9 for adults and $6.75 for children. Ticket sales for one movie showing totaled $1406.25.
What equation models the situation?
Adult ticket sales + _ ticket sales - total sales
9a + _ = 1406.25
What do the _ represent?
_ = number of adult tickets
c = number of child tickets

Word Bank:
Child
Variables
6.75a
a

1 answer

To model the scenario with a two-variable equation, we know the following:

The cost of an adult ticket is $9.
The cost of a child ticket is $6.75.
The total sales for one movie showing is $1406.25.

Let:

$ a $ = number of adult tickets sold
$ c $ = number of child tickets sold

The sales from adult tickets can be expressed as $ 9a $ and the sales from child tickets can be expressed as $ 6.75c $.

To represent the total ticket sales, the equation would be:

\[ 9a + 6.75c = 1406.25 \]

Thus, if we fill in the blank represented by "_": 9a + 6.75c = 1406.25

So, in this case, the "_" represents the sales from child tickets, which is $ 6.75c $.