Explanation:
I am not sure what the actual question is.
the general function for the amount of gathered reward points p with v visits to the theater is
p(v) = 14.5×v + 40 (40 starting points, 14.5 points per visit)
to know how many visits are needed for a certain amount of points (185) we need to solve that equation for v :
185 = 14.5×v + 40
145 = 14.5×v
v = 145/14.5 = 10
so, she needs at least 10 visits to gather the desired 185 points for a free ticket.
but that applies only to the first free ticket.
after that the function behavior kind of changes, because we have no more starting points :
so to get 2×185 = 370 points for 2 free tickets she will need
370 = 14.5×v + 40
330 = 14.5×v
v = 330/14.5 = 22.75862069...
we need to round up to the next whole number (because there can be no "part-visits").
so, she will need 23 visits for 2 free tickets (that means 13 more visits for the second free ticket).