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.

Answer 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