if y varies directly as x, and y is 180 when x is n and y is n when x is 5, what is the value of n? 6 18 30 36

Explanation:

Step1: Write direct - variation formula

Since (y) varies directly as (x), the formula is (y = kx), where (k) is the constant of variation. When (y = 180) and (x=n), we have (180=kn), so (k=\frac{180}{n}). When (y = n) and (x = 5), we have (n=k\times5), so (k=\frac{n}{5}).

Step2: Equate the two expressions for (k)

Set (\frac{180}{n}=\frac{n}{5}). Cross - multiply to get (n^{2}=180\times5).

Step3: Solve for (n)

(n^{2}=900). Taking the square root of both sides, (n=\pm30). But in the context of direct - variation problems with positive - valued variables usually considered, we take (n = 30).

Answer:

C. 30