Question

If `x` varies directly as `y` and inversely as `z` and when `y=7` and `z=2`, `x=14`, what is `x` when `y=16` and `z=4`?

Answer 1

`x=16`

Explanation:

`x` varies directly as `y` and inversely as `z` means `xpropy` and `xprop1/z` i.e.

`xpropy xx1/z`

In other words `x=kxxy/z` where `k` is a constant

Since when `y=7` and `z=2`, we have `x=14`, we have

`14=kxx7/2` and `k=14xx2/7=4`

and hence `x=4y/z`

and when `y=16` and `z=4`

`z=4xx16/4=16`

Answer 2

`x=16`

Explanation:

`"the initial statement is " xpropy/z`

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

`rArrx=kxxy/z=(ky)/z`

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

`x=14,y=7,z=2`

`x=(ky)/zrArrk=(xz)/y=(14xx2)/7=4`

`rArr"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(x=(4y)/z)color(white)(2/2)|)))`

`"when " y=16" and " z=4`

`rArrx=(4xx16)/4=16`