Question

If y varies inversely as x and y = 18 when x = 4, what is y when x = 24? a. 12 b. 6 c. 3 d. 16.

Answer 1

`\huge\boxed{\sf y = 3}`

Explanation:

Given that:

`\displaystyle y \propto (1)/(x)`

Converting proportionality into equality

`\displaystyle y = (k )/(x)` ------------------------- (1)

We know that:

y = 18 when x = 4

Put in Eq. (1)

`\displaystyle 18 = (k)/(4) \\\\Multiply \ 4 \ to \ both \ sides\\\\18 * 4 = k\\\\72 = k\\\\ \boxed{k = 72}`

Now,

y = ? when x = 24

Put in Eq. (1)

`\displaystyle y = (72)/(24) \\\\\boxed{y = 3}`

`\rule[225]{225}{2}`