If y varies directly as x and inversely as z, and $y=10$ when $x=4$ and $z=3$, find y when $x=7$ and $z=15$.

et3atissb
2022-04-21
Answered

If y varies directly as x and inversely as z, and $y=10$ when $x=4$ and $z=3$, find y when $x=7$ and $z=15$.

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drenkttj9

Answered 2022-04-22
Author has **20** answers

Step 1

Given

y varies directly as x

i.e.

$y\propto x$

and

abd inversely as z

$y\propto \frac{1}{4}$

Hence

$y\propto \frac{1}{4}$

$\Rightarrow y=\u22cf\frac{1}{4}$ ...(1)

Where 'k' is proportional constant

Step 2

Put $y=10,x=4\text{and}z=3$ in equation (1)

$10=k\times \frac{4}{3}$

$\Rightarrow k=\frac{30}{4}$

$\frac{15}{2}$ ...(2)

Now put $x=7$ and $z=15$ in equation(1),then

$y=k\times \frac{7}{15}$

$\Rightarrow y=\frac{15}{2}\times \frac{7}{15}$

$=\frac{7}{2}$

Step 3

Answer:

$y=\frac{7}{2}$

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