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?

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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?

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Answer 1 · 2017-11-08T13:39:15

$y = 60 x + \frac{90}{z} + 120 w$ $y=60x+90/z+120w$

Explanation:

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

The wording implies:

$y = k_{1} x$ $y=k_1x$

$x = \frac{k_{2}}{z}$ $x=k_2/z$

$color(white)()$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Consider the case$ $color(blue)("Consider the case")$
$y = k_{1} x d \to d 540 = k_{1} (30) \Rightarrow k_{1} = \frac{540}{30} = 180$ $y=k_1x color(white)("d")->color(white)("d")540= k_1(30) => k_1=540/30 = 180$

$y = 180 x$ $y=180x$

$color(white)()$

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

$Consider the case$ $color(blue)("Consider the case")$
$y = \frac{k_{2}}{z} d \to d 540 = \frac{k_{2}}{5} \Rightarrow k_{2} = 5 \times 540 = 2700$ $y=k_2/z color(white)("d")->color(white)("d")540= k_2/(5) => k_2=5xx540= 2700$

$y = \frac{2700}{z}$ $y=2700/z$

$color(white)()$

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

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

Observe that $d 2 \times 15 = 30$ $color(white)("d")2xx15=30$
$ddddddd \Rightarrow d 2 \times w = x$ $color(white)("ddddddd")=>color(white)("d") 2xxw=x$

Thus $d y = k_{1} x d \to d y = k_{1} (2 w)$ $color(white)("d")y=k_1xcolor(white)("d")->color(white)("d")y=k_1(2w)$

as $k_{1} = 180$ $k_1=180$ then we have:

$dddddddddddd \to d y = 180 (2 w)$ $color(white)("dddddddddddd")->color(white)("d")y=180(2w)$

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

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

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

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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?

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