Answer:
Combined equation is [tex]a = \frac{kb}{c}[/tex]
Step-by-step explanation:
a varies directly as b and inversely as c.
This can be written as
a =[tex]k \times b[/tex]
a = kb
where k is the proportionality constant
[tex]a = \frac{kb}{c}[/tex]-------------------------------------(1)
Now lets find the k value bu substituting the given a, b,c values
[tex]4 = \frac{k (12)}{9}[/tex]
[tex]9 \times 4 = 12k[/tex]
36 = 12 k
[tex]k = \frac{36}{12}[/tex]
k = 3
Thus the eq(1) becomes
[tex]a = \frac{3b}{c}[/tex]
Let us now find the value of a when b=7 and c = 3
[tex]a = \frac{3(7)}{3}[/tex]
[tex]a =\frac{21}{7}[/tex]
a = 7
