Question

If y varies inversely as x and y = 32 when x = 42, find y when x = 24.

Answer 1

Answer:

$\boxed{y=56}$

Explanation:

When talking about the concept of Inversely proportional we mean that if all other variables are held constant one variable decreases if the other variable increases. So, $y$ varies inversely as $x$ or $y$ is inversely proportional to $x$ if and only if:

$y=\frac{k}{x} \\ \\ For \ some \ nonzero \ constant \ k$

Where $k$ is the constant of variation or the constant of proportionality.

From the problem, we know that:

$When \ x=42, \ y=32$

So we can find $k$:

$y=\frac{k}{x} \\ \\ 32=\frac{k}{42} \therefore k=32 \times 42 \therefore k=1344$

So we need to find:

$y \\ \\ When \ x=24$

Therefore:

$y=\frac{1344}{24} \\ \\ \boxed{y=56}$