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A quantity p is partly constant and partly varies inversely as a quantity q.Given that p=10 when q=1.5 and p=20 when q=1.25, find the value of p when q=0.5.

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  1. p = c + k/q

    10 = c + k/1.5
    20 = c + k/1.25
    -----------------------subtract
    -10 = k (1/1.5 - 1/1.25) = k (0.6667 - 0.80) = -k (0.13333)
    k = 75
    then
    10 = c +75/1.5 = c + 50
    c = -40
    so
    p = -40 + 75/q
    if q = 0.5
    p = -40 + 150 = 110

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