Question

Suppose that y varies jointly with w and x and inversely with z and y=360 when w=8, x=25 and z=5. How do you write the equation that models the relationship. Then find y when w=4, x=4 and z=3?

Answer 1

`y =48` under the given conditions
(see below for the modelling)

Explanation:

If `color(red)y` varies jointly with `color(blue)w` and `color(green)x` and inversely with `color(magenta)z`
then
`color(white)("XXX")(color(red)y * color(magenta)z)/(color(blue)w *color(green)x) = color(brown)k` for some constant `color(brown)k`

GIven
`color(white)("XXX")color(red)(y=360)`
`color(white)("XXX")color(blue)(w=8)`
`color(white)("XXX")color(green)(x=25)`
`color(white)("XXX")color(magenta)(z=5)`

`color(brown)k=(color(red)(360) * color(magenta)(5))/(color(blue)(8) * color(green)(25))`

`color(white)("XX")=(cancel(360)^45 * cancel(5))/(cancel(8) * cancel(25)_5`

`color(white)("XX")= color(brown)9`

So when
`color(white)("XXX")color(blue)(w=4)`
`color(white)("XXX")color(green)(x=4)` and
`color(white)("XXX")color(magenta)(z=3)`

`color(white)("XXX")(color(red)y * color(magenta)3)/(color(blue)4 * color(green)4) = color(brown)9`

`color(white)("XXX")color(red)y = (color(brown)9 * color(blue)4 * color(green)4)/color(magenta)3 = 48`