Question

If y varies inversely as x and y=6 when x=2, what is x when y=60?
1/5
5
120

Answer 1

x =
`(1)/(5)`

Explanation:

Given that y varies inversely as x then the equation relating them is

y =
`(k)/(x)` ← k is the constant of variation

To find k use the condition y = 6 when x = 2, then

k = yx = 6 × 2 = 12

y =
`(12)/(x)` ← equation of variation

When y = 60, then

60 =
`(12)/(x)` ( multiply both sides by x )

60x = 12 ( divide both sides by 60 )

x =
`(12)/(60)` =
`(1)/(5)`

Answer 2

x = 1/5.

Explanation:

y = k/x where k is a constant.

When y = 6, x = 2 so we have:

6 = k/2

k = 12.

So the relation is y = 12/x.

When y = 60:

60 = 12/x

6x = 12

x = 12/60

x = 1/5.