Question

If z varies directly as x and inversely as y, and z = 8 when x = 12 and y = 3, the value of the constant of proportionality is what number?

Answer 1

`k=2`

Explanation:

when z varies directly proportional to x means a division

`c=z/x` where c is a constant of proportionality

when z varies inversely proportional to x it means a product

`zy=c`

now with both

`k=(zy)/x`

`z=8; x=12 and y=3`

`k=(8.3)/12`

`k=2`

Answer 2

`k=2`

Explanation:

`"the initial statement is "zpropx/y`

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

`rArrz=kxx x/y=(kx)/y`

`"to find k use the given condition"`

`z=8" when "x=12" and "y=3`

`z=(kx)/yrArrk=(yz)/x=(3xx8)/12=24/12=2`