   SEARCH HOME Math Central Quandaries & Queries  Hi I'm Rene, I'm stuck with some problems in direct and inverse variation. I know how to solve direct and inverse problems when only one variation is in a question at a time. EX: p varies inversely as the square root of q, and when p=12, q=36 find p when q=16 12*6 =p*4 72=4p 18=p But how would you solve a problem like..... If s varies directly as r and inversely as t, and s=10 when r=5 and t=3, for what value of t will s=3 when r=4 ? Hi Rene,

I would approach the first problem this way.

Since p varies inversely as the square root of q I know that

p √q = k for some constant k.

Substitute p = 12 and q = 36 to find k (k = 72) so you know that

p √q = 72

Now substitute q = 16 and solve for p.

If the question had said "a varies directly as b" I would have started with

a = k b for some constant k.

But you have "s varies directly as r and inversely as t" so I would start with

s t = k r for some constant k.

Substitute the values you know for s, r and t to find k.

I hope this helps,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.