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You can first find the second \(a\), by setting up an equation and solving it. We can make the equation \(\frac{2}{5} = \frac{a}{3}\), which we can solve using cross-multiplication. Then, we get \(6 = 5a\), which gives us \(a = \frac{6}{5}\). So if \(a = \frac{6}{5}\), and \(a\) is inversely proportional to \(c\), than we can see that \(\frac{6}{5} \times c\) must equal \(18\), because \(2 \times 9 = 18\). \(\frac{18}{\frac{6}{5}} = 18 \times \frac{5}{6} = 15\). So \(c = 15\).

- Daisy

2 = 5k
k=2/5 constant of direct proportionality. But:............................(1)
2 =k/9
k=18 constant of inverse proportionality. But when:..................(2)
b =3, from (1) above:
a =2/5 x 3=6/5 = 1.2.  Using (2) above for the new value of a:
1.2 =18 / c
c = 18 / 1.2
c =15 when b = 3 

Look at this problem in a much simpler and intuitive way as follows:

When "b" = 5 goes to "b"= 3, that is a direct decrease of 3/5 =0.6, when c=9

And since "b" is directly proportional to "a" and inversely proportional to "c", it follows that:

New "c" = 9 x 1/0.6 =15