Question

Suppose y varies directly with x. If x is 30 when y is 10, what is x when y is 9?

Answer 1

When y varies directly with x, it means that both x and y are directly proportional.

And then y is directly proportional to x, which menas for ecample, that when x doubles, y doubles too. If x halves, y halves as well.

Also, the ratio of the two measures x and y is always costant

So, $\frac{y}{x} = k$ (k is the costant)

Now, let's find the costant...10/30 = $0. \overline {3}$

Since we have a recurring decimal, trasform it in a fraction -> 3/9 semplified 1/3

From the formula y/x = k, we find the formula x = y/k

x = $9 : \frac{1}{3}$ = $9 * 3 = 27$

So x = 27, hope I got it right

Answer 2

When y and x vary directly X= 3 when y = 9