Question

1. For the Summer R&B/Soul Festival, there is one price for students, one for adults, and another for senior citizens. The Jackson family bought 3 student tickets and 2 adult tickets for $104. The Williams family bought 5 student tickets, 1 adult ticket, and 2 senior citizen tickets for $155. The Mullins family bought 2 of each for $126. a. Write a system of equations that can be used to find the cost of each ticket. b. Solve the system by elimination to find the cost of each ticket.

Answer 1

Explanation:

Let's call student tickets s, adult tickets a and senior tickets c. The equations for each family are as follows:

Jackson: 3s + 2a = 104

Williams: 5s + 1a + 2c = 155

Mullins: 2s + 2a + 2c = 126

To get started, let's solve the Jackson family equation for a:

2a = 104 - 3s so

a = 52 - 1.5s

Now we can use that a value in the Williams equation:

5s + 1(52 - 1.5s) + 2c = 155 and

5s + 52 - 1.5s + 2c = 155 and

3.5s + 2c = 103

We can also use that a value in the Mullins equation:

2s + 2(52 - 1.5s) + 2c = 126 and

2s + 104 - 3s + 2c = 126 so

-1s + 2c = 22

Solve the system that is in bold print now by multiplying the Mullins equation through by -1 to get a new system that looks like this:

3.5s + 2c = 103

1s - 2c = -22

The c's eliminate each other leaving us with only s's:

4.5s = 81 so

s = 18

The cost of a student ticket is $18. Now use that $18 in place of s in the first bold equation above:

3.5(18) + 2c = 103 and

63 + 2c = 103 and

2c = 40 so

c = 20

The cost of a senor ticket is $20. Now use both of those values in the Williams equation at the beginning to solve for a:

5(18) + 1a + 2(20) = 155 and

90 + 1a + 40 = 155 and

1a = 25

The cost of an adult ticket is $25