Answer:
The value of b is 5/6
Step-by-step explanation:
The relationship stated as "a varies directly as b and inversely as c" can be written as:
[tex]\displaystyle a=k\frac{b}{c}[/tex]
Where k is the constant of proportionality. We need to find its value by plugging in the given condition: b=12 when c=3 and a=96:
[tex]\displaystyle 96=k\frac{12}{3}=4k[/tex]
Solving for k:
[tex]k=96/4=24[/tex]
The relation is now written as:
[tex]\displaystyle a=24\frac{b}{c}[/tex]
Now we find the value of b when a=5 and c=4. Solving for b:
[tex]\displaystyle b=\frac{ac}{24}[/tex]
[tex]\displaystyle b=\frac{5*4}{24}=\frac{5}{6}[/tex]
The value of b is 5/6
