Question

If q varies directly as r and inversely as s. When r = 12 and s = 16, q is 72. For what value of r will q = 192 when s = 17?

Answer 1

`r=34`

Explanation:

If q varies directly with r and inversely with s, then we have an equation like this:

`q=(ar)/s` where `a` is a constant

So, we first need to solve for `a`.

Knowing what they give us, we substitute in:

`72=(a*12)/16`
`72*color(red)(16)=(12a*color(red)(16))/16`
`(72*16)/color(red)(12)=(12a)/color(red)(12)`
`a=96`

So, now let's solve for r given what we know:

`192=(96*r)/17`
`192*color(red)(17)=(96*r*color(red)(17))/17`
`(192*17)/color(red)(96)=(96r)/color(red)(96)`
`34=r`

Hope this helps!