JAMB - Mathematics (2014 - No. 14)
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.
\(P = \frac{Q}{12R}\)
\(P = \frac{12Q}{R}\)
\(P = 12QR\)
\(P = \frac{12}{QR}\)
Explanation
\(P \propto \frac{Q}{R}\)
\(P = K \frac{Q}{R}\)
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
\(P = \frac{12Q}{R}\)
\(P = K \frac{Q}{R}\)
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
\(P = \frac{12Q}{R}\)
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