Question

Assume that y varies inversely with x. If y= 1.6 when x= 0.5, find x when y= 3.2

Answer 1

x = 0.25

Explanation:

If y varies inversely with x, then:

`y \propto (1)/(x) \implies y=(k)/(x) \quad \textsf{(for some constant k)}`

Given:

• y = 1.6 when x = 0.5

Substitute the given values into the found equation and solve for k:

`\implies 1.6=(k)/(0.5)`

`\implies k=1.6(0.5)`

`\implies k=0.8`

Therefore:

`y=(0.8)/(x)`

To find the value of x when y = 3.2, substitute y = 3.2 into the found equation and solve for x:

`\implies 3.2=(0.8)/(x)`

`\implies x=(0.8)/(3.2)`

`\implies x=0.25`