Question

Find an equation of combined variation where a varies directly as b and inversely as c. One set of values is a = 4, b = 12, and c = 9. Find a when b = 7 and c = 3.

Answer 1

Answer:

Combined equation is  $a = \frac{kb}{c}$

Step-by-step explanation:

a varies directly as b and  inversely as c.

This can be written as

a =$k \times b$

a =  kb

where k is the proportionality constant

$a = \frac{kb}{c}$-------------------------------------(1)

Now lets find the k value bu substituting the given a, b,c values

$4 = \frac{k (12)}{9}$

$9 \times 4 = 12k$

36 =  12 k

$k = \frac{36}{12}$

k = 3

Thus the eq(1) becomes

$a = \frac{3b}{c}$

Let us now find the value of a  when b=7  and c = 3

$a = \frac{3(7)}{3}$

$a =\frac{21}{7}$

a = 7