Question

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 senior citizen tickets and 4 child tickets for a total of $68. The school took in $59 on the second day by selling 3 senior citizen tickets and 7 child tickets.

Define variables and write a system of equations that model the situation.

What is the price each of one senior citizen ticket and one child ticket?

On the third day of ticket sales, no senior citizens purchased tickets. Make a table to determine how many tickets would need to be sold in order to make at least $35?

Answer 1

Child Ticket=$5

Senior Citizen Ticket=$8

7 Tickets

Explanation:

Child ticket=c, Senior Citizen ticket=s

Now create the equations

6s+4c=68

3s+7c=59

Let's multiply the second equation by -2 so we can solve this system of equations by addition.

6s+4c=68

-6s-14c=-118

Add them together keeping like terms together.

6s-6s+4c-14c=68-118

Simplify

-10c=-50

c=5

To find s, put 5 in for c in one of the equations.

6s+4(5)=68

Simplify

6s+20=68

6s=68-20

6s=48

s=8

Since no senior citizens purchased tickets on the third day, the total of children's tickets must equal $35

5c=35

c=7

7 tickets

Answer 2

Let's define variables to represent the unknowns:Let S be the price of one senior citizen ticket.

Let C be the price of one child ticket.Now, let's set up a system of equations based on the information given:On the first day:

6S+4C=68On the second day:

3S+7C=59

These equations represent the total revenue from ticket sales on each day.To find the prices of one senior citizen ticket (S) and one child ticket (C), you can solve this system of equations.Now, for the third day, where no senior citizens purchased tickets and the goal is to make at least $35, we can set up an inequality:7C≥35This inequality represents the condition that the total revenue from child tickets (7C) should be greater than or equal to $35.

To find out how many child tickets need to be sold to make at least $35, you can solve this inequality for C. Once you have the value for C, you can use it to find the total revenue on the third day (7C.

Explanation: