Answer:
[tex]\boxed{y=56}[/tex]
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, [tex]y[/tex] varies inversely as [tex]x[/tex] or [tex]y[/tex] is inversely proportional to [tex]x[/tex] if and only if:
[tex]y=\frac{k}{x} \\ \\ For \ some \ nonzero \ constant \ k[/tex]
Where [tex]k[/tex] is the constant of variation or the constant of proportionality.
From the problem, we know that:
[tex]When \ x=42, \ y=32[/tex]
So we can find [tex]k[/tex]:
[tex]y=\frac{k}{x} \\ \\ 32=\frac{k}{42} \therefore k=32 \times 42 \therefore k=1344[/tex]
So we need to find:
[tex]y \\ \\ When \ x=24[/tex]
Therefore:
[tex]y=\frac{1344}{24} \\ \\ \boxed{y=56} [/tex]
