Alright, let's solve this step-by-step.
### Given Information:
1. Erin has [tex]$22 left after taking 1 ride.
2. Erin has $[/tex]16 left after taking 3 rides.
Let's use this information to find the cost of one ride and the total money Erin brought.
Let's denote:
- [tex]\( r \)[/tex] as the cost of one ride.
- [tex]\( m \)[/tex] as the total money Erin brought to the carnival.
### Part A: Finding the Cost of One Ride
1. After 1 ride, Erin had [tex]$22 left.
\[
m - r = 22 \quad \text{(Equation 1)}
\]
2. After 3 rides, Erin had $[/tex]16 left.
[tex]\[
m - 3r = 16 \quad \text{(Equation 2)}
\][/tex]
We now have a system of two equations:
[tex]\[
m - r = 22 \tag{1}
\][/tex]
[tex]\[
m - 3r = 16 \tag{2}
\][/tex]
To find [tex]\( r \)[/tex], we can solve this system of equations by elimination or substitution. Let's use elimination:
Subtract Equation (2) from Equation (1):
[tex]\[
(m - r) - (m - 3r) = 22 - 16
\][/tex]
Simplify:
[tex]\[
m - r - m + 3r = 6
\][/tex]
[tex]\[
2r = 6
\][/tex]
[tex]\[
r = 3
\][/tex]
So, the cost of one ride is [tex]$3.
### Part B: Finding the Total Money Erin Brought to the Carnival
Now, we substitute \( r = 3 \) back into either Equation (1) or Equation (2) to find \( m \). Let's use Equation (1):
\[
m - r = 22
\]
\[
m - 3 = 22
\]
\[
m = 25
\]
So, Erin brought $[/tex]25 to the carnival.
### Summary:
Part A: The cost of one ride is [tex]$3.
Part B: Erin brought $[/tex]25 to the carnival.
