Respuesta :

Hagrid
The first statement "y varies directly as x" means that as y increases, x also increases. To help us we need to assign a proportionality constant, k. We can now say:
y=kx where k is just a constant. Then substitute the values, 

180=kn
n=5k

With these equation we know that k is equal to (positive or negative) 6 and therefore we can get n to be (positive or negative)  30. 

Answer

Find out the value of n .

To proof

As given

y varies directly as x

thus

[tex]y \propto x[/tex]

y = kx

Where k is the constant of proportionality .

As given

y is 180 when x is n

180 = kn

[tex]k = \frac{180}{n}[/tex]

y is n when x is 5

n = 5k

[tex]k = \frac{n}{5}[/tex]

Compare the value of k .

[tex]\frac{180}{n} = \frac{n}{5}[/tex]

solving

n² = 900

n = √900

n = 30

Therefore the value of n is 30 .

Hence proved