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

Find out the value of n .

To proof

As given

y varies directly as x

thus

`y \propto x`

y = kx

Where k is the constant of proportionality .

As given

y is 180 when x is n

180 = kn

`k = (180)/(n)`

y is n when x is 5

n = 5k

`k = (n)/(5)`

Compare the value of k .

`(180)/(n) = (n)/(5)`

solving

n² = 900

n = √900

n = 30

Therefore the value of n is 30 .

Hence proved

Answer 2

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.