Question

If y=21 when x=-6, how do you find x when y=7 given that y varies inversely as x?

Answer 1

`x=-18`

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 given condition"`

`y=21" when "x=-6`

`y=k/xrArrk=yx=21xx-6=-126`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=-126/x)color(white)(2/2)|)))`

`"when "y=7`

`x=-126/y=-126/7=-18`

Answer 2

`x= -18`

Explanation:

`y prop 1/x or y = k*1/x or x*y = k ; k` is constant of proportionality.

`y=21 . x= -6 :. k = x* y =-6 * 21 = -126` .

So the variation equation is `x * y = -126 ; y=7, x = ?`

`:. x * 7 = -126 :. x = -126/7 = -18`

`x= -18` [Ans]