Question

Suppose a varies directly as b and inversely as c. Find b when a = 5 and 4, if b = 12 when

C3 and a = 96

Answer 1

The value of b is 5/6

Explanation:

The relationship stated as "a varies directly as b and inversely as c" can be written as:

`\displaystyle a=k(b)/(c)`

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:

`\displaystyle 96=k(12)/(3)=4k`

Solving for k:

`k=96/4=24`

The relation is now written as:

`\displaystyle a=24(b)/(c)`

Now we find the value of b when a=5 and c=4. Solving for b:

`\displaystyle b=(ac)/(24)`

`\displaystyle b=(5*4)/(24)=(5)/(6)`

The value of b is 5/6