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?

1 Answer
Dec 10, 2017

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!