we have that
the equation 1 is equal to
C=1.25r+5
Equation 2 is
C=r+10
Equate both equations
1.25r+5=r+10
solve for r
1.25r-r=10-5
0.25r=5
r=20
Find the value of C for r=20 rides
C=r+10
C=20+10=$30
Note: The result is the same if you use equation 1
so
C=1.25(20) +5
C=$30
therefore
the answer is
r=20 rides and the cost is C=$30