Question

Tickets to a production cost $10.00 for general admission or $8.00 with student identification. If 184 people paid to see a performance and $1624 was collected, how many of each type of admission were sold? - Define & identify variables, write two systems of equations. - Solve by substitution. Show work.

a) x = number of general admission tickets; y = number of student tickets
b) x = number of student tickets; y = number of general admission tickets
c) x = number of adult tickets; y = number of child tickets
d) x = number of child tickets; y = number of adult tickets

Answer 1

Using a system of linear equations, we determined that 76 general admission tickets and 108 student tickets were sold, based on the total number of tickets sold (184) and total money collected ($1624).

Step-by-step explanation:

To solve the problem regarding the number of general admission and student tickets sold, we can set up a system of linear equations. We’ll define our variables as follows for one version of the system:

• x = number of general admission tickets
• y = number of student tickets

We have two pieces of information that will help us set up our equations:

1. The total number of tickets sold was 184.
2. The total amount of money collected was $1624.

Using the given information, we can construct the following equations:

1. x + y = 184 (The total number of tickets)
2. $10x + $8y = $1624 (The total amount of money collected)

Let's solve the system by substitution. First, we can express x from the first equation:

x = 184 - y

Now, we substitute x in the second equation:

$10(184 - y) + $8y = $1624

Simplify and solve for y:

$1840 - $10y + $8y = $1624

$1840 - $2y = $1624

$2y = $1840 - $1624

$2y = $216

y = $216 / $2

y = 108

Now, we can find x:

x = 184 - y

x = 184 - 108

x = 76

Therefore, 76 general admission and 108 student tickets were sold.