Inverse math question

The cost per student of a camping trip varies inversely as the number of students attend. It will cost each $95 if 22 students attend. How many students would have to attend to get the cost down to $58.06?

let "The cost per student of a camping trip" = x
and "the number of students attend" = y

the question gives that x varies inversely as y.
Therefore let the variation constant of the problem be "a".
And you get a = xy

with first event, you get a = 95 * 22

with second event and the values of variation constant "a" you get from the first event,

you get 95 * 22 = 58.06 * y

and you can get the answer by solving the equation

your final answer is approximate 36 students.(35.9972442301068......)

Cost varies inversely as the number of students
so C = k/n where C is cost and n is the number of students and k is the constant.
so $95 = k/22 or k = 95x22
so for the second part, n = k/C = 95 x 22 / $58.06 = 35.99724....
or the number of students that would need to attend to get the cost down to $58.06 is 36.

C = cost per student
n = number of students

C = k/n

95 = k/22
k = 95*22 = 2090

C = 2090/n

Now find n so that C = 58.06
58.06 = 2090/n
n = 2090/58.06
n = 35.99724423

36 students would have to attend

95 * 22 = k
k = 2090

58.06 * x = 2090
x = 2090/58.06

x = 36