Question

This is the two that go together, but are separate questions

Answer 1

Answers:

Option 1)

6a + 8s = 102

14a + 4s = 150

each adult ticket costs 9 dollars

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Step-by-step explanation:

6 adult tickets and 8 student tickets bring in $102, so that means 6a+8s = 102

14 adult tickets and 4 students tickets bring in $150, so 14a+4s = 150

The system of equations is

`\begin{cases}6a+8s = 102\\14a+4s = 150\end{cases}`

If we multiply both sides of the second equation by -2, we get this updated system

`\begin{cases}6a+8s = 102\\-28a-8s = -300\end{cases}`

Add the equations straight down

6a+(-28a) = -22a

8s+(-8s) = 0s = 0 ... the 's' terms go away

102+(-300) = -198

So we end up with the equation -22a = -198 and that solves to a = 9 after dividing both sides by -22.

Each adult ticket costs $9

If you want the value of s, then

6a+8s = 102

6(9)+8s = 102

54 + 8s = 102

8s = 102-54

8s = 48

s = 48/8

s = 6

Meaning each student ticket costs $6

Or you could use the other equation

14a+4s = 150

14(9)+4s = 150

126+4s = 150

4s = 150-126

4s = 24

s = 24/4

s = 6

We get the same value of s