Math Help - Help check please

Suppose y varies inversely as x and y =24 when x= 3. Find x when y = 36.

So I worked it out I got this:

36 -24 = x - 3
12+3 = 15
15 =x

y=36 , x=15

Is this right?

"y varies inversely as x "

y ----> 1/x
y = k(1/x) ----the equation.

y=24 when x=3, so,
24 = k(1/3)
24 = k/3
24*3 = k
k = 72

Hence, when y = 36,
36 = 72(1/x)
36 = 72/x
36x = 72
x = 72/36 = 2 ---answer.

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Another meaning of "y varies inversely as x" is:
if x goes higher, then y goes lower; if x goes lower, then y goes higher...proportionately.

thank you