If y varies directly as x and inversely as z,

Question

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 $z = 15$ .

Answer 1

Step 1
Given
y varies directly as x
i.e.
$y \propto x$
and
abd inversely as z
$y \propto \frac{1}{4}$
Hence
$y \propto \frac{1}{4}$
$\Rightarrow y = ⋏ \frac{1}{4}$ ...(1)
Where 'k' is proportional constant
Step 2
Put $y = 10, x = 4 and z = 3$ 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:
$y = \frac{7}{2}$

If y varies directly as x and inversely as z,

Answers (1)

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