Question

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?

Answer 1

"something" varies directly to "something else" means
 "something" = "some value" * "something else"
        y = "some value" * x
        y = (a) x
  y = (n)x
y=180, x=n⟹180=(a)n
y=n,x=5⟹n=(a)5
Thus 180=(a)n⟹180/n=a
Therefore,
n=(a)5⟹n=(180/n)5

The correct value of 'n' is 30.

Answer 2

Answer:

The value of n for this relation is 30

Step-by-step explanation:

If y varies directly as x, this means that the relation between y and x can be stated as a linear relation of the kind:

y=mx

In the equation, m must be a number, to know exact relation. The two situations that are given can be stated as:

180=m.n

n=m.5

Note that are two unknowns quantities in the equation, m and n. In this particular problem, we must find n. To doing this, we will solve the equation for m:

180=m.n → m =180/n

n=m.5 → m = n/5

As m in both equations must be equal:

m = m  

180/n = n/5

180*5 = n*n

900=n^2 → n = 30