Question

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

Answer 1

`\boxed{y=56}`

Step-by-step 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=(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=(k)/(x) \\ \\ 32=(k)/(42) \therefore k=32 * 42 \therefore k=1344`

So we need to find:

`y \\ \\ When \ x=24`

Therefore:

`y=(1344)/(24) \\ \\ \boxed{y=56}`