Answer:
Step-by-step 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
