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A quantity P varies partly as Q and partly as the square root of Q, given that P=30 when Q=9, and P=14 when Q=16. Find P when Q=36.

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Let L and K be constants.
P=LQ + K √Q
30 = 9L + √9K
14 = 162 + √16 K
2K + 62 = 20
2K + 8L = 7
-2L = 13
L = -13/2
K + 3(-13/2) = 10
K = 10/1 + 392 = 59/2
P = -13/2Q = 59/2 √Q
P = -13/2 x 36 + 59/2 x √36
P = -234 + 177 = -57

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