Question

Assume y varies inversely as x, if y=8 when x=4, how do you find x when y=2?

Answer 1

`x=16`

Explanation:

`y" varies inversely as "x=>yprop1/x`

`=>y=k/x" where "k" is the constant of proportionality"`

`y=8, x=4`

we have

`8=k/4=>k=8xx4=32`

`:.y=32/x`

`y=2`

`2=32/x=>x=32/2=16`

`x=16`

Answer 2

`x=16`

Explanation:

`"the initial statement is " yprop1/x`

`"to convert to an equation multiply by k, the constant "`
`"of variation"`

`rArry=kxx1/x=k/x`

`"to find k, use the condition given for x and y"`

`y=8" when " x=4`

`y=k/xrArrk=xy=4xx8=32`

`"the equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=32/x)color(white)(2/2)|)))`

`"when y = 2"`

`xy=32rArrx=32/y=32/2=16`