Suppose a is directly proportional to b, but inversely proportional to c. If a = 2 when b = 5 and c = 9, then what is c when b =3?

Logic
Aug 23, 2018

#1**+4 **

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

dierdurst
Aug 23, 2018

#2**+1 **

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**

Guest Aug 24, 2018

edited by
Guest
Aug 24, 2018