Question

At the movie theater, child admission is $5.20 and adult admission is $9.30
. On Saturday, 151 tickets were sold for a total sales of $1035.30
. How many adult tickets were sold that day?

Answer 1

Answer: 61 adult tickets.

Step-by-step explanation:

Set up a system of equations, where:

c: is the number of child tickets sold on Saturday.

a: is the number of adult tickets sold on Saturday.

Then:

$\left \{ {{c+a=151} \atop {5.20c+9.30a=1035.30}} \right.$

By the Elimination method: Multiply the first equation by -5.20, then add the equations and solve for "a":

$(-5.20c-5.20a=-785.2)\\(5.20c+9.30a=1035.30)\\.................................................\\0c+4.1a=250.1\\4.1a=250.1\\a=\frac{250.1}{4.1}\\\\a=61$

Therefore, 61 adults tickets were sold that day.

Answer 2

This is a system of equations. Let's call each child ticket sold C and each adult ticket A. The total number of tickets purchased is C+A=151. We also know the total sales, which is calculated via the equation 5.20C+9.30A=1035.30.

Now just solve for the variables.

C+A=151

C=151-A

5.2C+9.3A=1035.30

5.2(151-A)+9.3A=1035.30

785.2-5.2A+9.3A=1035.304

4.1A=250.1

A=61

Now we know that 61 adult tickets were sold. To find the number of child tickets sold, just plug this back into the first equation.

C=151-A=151-61=90

So, 61 adult tickets and 91 child tickets were sold. Hope this helped!