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!