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

what's the value for "n"? we dunno
but we know that \(\bf y = 180, \quad x=n\implies \color{red}{180=(a)n}\\ \quad \\
y =n, \quad x = 5\implies \color{red}{n=(a)5}\\ \quad \\
thus\qquad 180=(a)n\implies \cfrac{180}{n}=a\qquad therefore\\ \quad \\
n=(a)5\implies n =\left(\cfrac{180}{n}\right)5\)

solve for "n"