Question

`z` is directly proportional to `x` and `y`. If when `x=6` and `y=8`, then `z=48`, then what is `z`, when `x=10` and `y=12`?

Answer 1

`z=120`

Explanation:

`z` varies jointly as `x` and `y` means `zpropx` and `zpropy` i.e.

`zpropx xxy`

In other words `z=kxx xy` where `k` is a constant

Since when `x=6` and `y=8`, w have `z=48`, we have

`48=kx6xx8` and `k=48/(6xx8)=48/48=1`

and hence `z=xy`

and when `x=10` and `y=12`

`z=10xx12=120`

Answer 2

`z=120`

Explanation:

`"the initial statement is " zpropxy`

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

`rArrz=kxy`

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

`x=6,y=8" when " z=48`

`z=kxyrArrk=z/(xy)=48/(6xx8)=1`

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

`"when " x=10" and " y=12`

`z=10xx12=120`