We have to express this problem as a system of equations.
The variables are cost "y" and the number of rides "x".
The first equation represents the cost for the unlimited rides.
The cost "y" is a constant value of $40 for any value of x, so it can be written as:
[tex]y=40[/tex]The second option correspond to a fixed cost of $15 and a variable cost of $1 per ride.
Then, we can write the cost as:
[tex]y=15+1\cdot x=15+x[/tex]If we want to graph the equations, we can see that the first equation is an horizontal line at $40.
The second equation is a line that has a y-intercept at y = 15 and a slope of 1.
We can graph them as:
The intersection seems to be at x = 25 rides.
We can check with the equations as:
[tex]\begin{gathered} y=y \\ 40=15+x \\ x=40-15 \\ x=25 \end{gathered}[/tex]Answer: the two options have the same cost for 25 rides.
