Direct and inverse variation

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

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