please help with math?

Question

If y varies directly as the cube of x and y = 30 when x = 2, find x when y = 468.75.

Answer 1

If y varies directly as the cube of x, then

y=kx^3, where k is the constant of proportionality

Given, y=30, when x=2, then

30=k*8,so,

k=30/8, =15/4, so,

y=15/4 x^3, so, when y=468.75, then,

468.75=15/4 x^3, so,

468.75*4/15=x^3,so,

125=x^3, so,

x=5. Hope this helps, Twiggy.

Answer 2

If y varies as the cube of x, then y/(x^3) is a constant. So...

30/(2^3) = 468.75/(x^3)

30x^3 = 468.75 * 8
x^3 = 125
x = 5