Question

Suppose that y varies jointly with x and x inversely with z and y=540 when w=15, x=30, and z=5, how do you write the equation that models the relationship?

Answer 1

`y=60x+90/z+120w`

Explanation:

You have only referenced `w` by its value and not included any anything linking it to `y`. So I am going to make an assumption about it.

The wording implies:

`y=k_1x`

`x=k_2/z`

`color(white)()`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider the case")`
#y=k_1x color(white)("d")->color(white)("d")540= k_1(30) => k_1=540/30 = 180#

`y=180x`

`color(white)()`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Consider the case")`
#y=k_2/z color(white)("d")->color(white)("d")540= k_2/(5) => k_2=5xx540= 2700#

`y=2700/z`

`color(white)()`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Consider the case "w=15)`

Observe that `color(white)("d")2xx15=30`
`color(white)("ddddddd")=>color(white)("d") 2xxw=x`

Thus `color(white)("d")y=k_1xcolor(white)("d")->color(white)("d")y=k_1(2w)`

as `k_1=180` then we have:

`color(white)("dddddddddddd")->color(white)("d")y=180(2w)`

`color(white)("dddddddddddd")->color(white)("d")y=360w`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Constructing "ul("an equation")" that links all three")`

There are a number of equation structures that can link `w,x,y and z`

Lets pick on the most strait forward.

`y=180x=270/z=360w`

So we have: `color(white)("d")3y=180x+270/z+360w`

Notice that 3, 18, 27 and 36 are all exactly divisible by 3. Consequently 180, 270 and 360 are also exactly divisible by 3

Dividing all of both sides by 3

`y=60x+90/z+120w`