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?

Solution:

Given y = 180 when x = n

Given: y ∝ x

⇒ y = kx (direct proportion) 

And y\(_1\) = 180 when x\(_1\) = n

y\(_2\) = n when x\(_2\) = 5

thus we have y\(_1\)/ x\(_1\)= y\(_2\)/ x\(_2\)

⇒ 180/n = n/5

⇒ n² = (180)5

⇒ n² = 900

⇒ √n² = √900

⇒ n = ±30

⇒ n = 30 and n = -30

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?

Summary:

If y varies directly as x, and y is 180 when x is n and y is n when x is 5 then the value of n is solved as 30 and -30.