P varies directly as Q and inversely as R. ..

Question 1 Report

P varies directly as Q and inversely as R. When Q = 36 and R = 16, P = 27. Find the relation between P, Q and R.

P = \frac{Q}{12 R}

P = \frac{12 Q}{R}

P = 12 Q R

P = \frac{12}{Q R}

Answer Details

$P \propto \frac{Q}{R}$
$P = K \frac{Q}{R}$
When Q = 36, R = 16, P = 27
Then substitute into the equation
$27 = K \frac{36}{16}$

$K = \frac{27 \times 16}{36}$
$K = 12$
So the equation connecting P, Q and R is
$P = \frac{12 Q}{R}$