Question

When a = 6 and b = 22, c = 33. If c varies directly with b and inversely with a, which equation models the situation?

Answer 1

c= 9b/a

Explanation:

The statement "y varies directly as x," means that when x increases, y increases by the same factor. The statement "y varies inversely as x means that when x increases, ydecreases by the same factor.

Then, we can say that:

c ∝ b, thus c= kb and c = k/a.

Using both equations we have that:

c= kb/a

Given that a=6, b=22 and c=33 we have that:

33 = 22k/6

Solving for k:

k=9.

Then the equation that models the situation is:

c= 9b/a

Answer 2

c = 9b/c

Explanation:

If c varies directly with b and inversely with a, then this may be written mathematically as;

c = kb/a

Therefore;

k = ac/b

Hence in this case;

k = (6 × 33)/22

= k

Therefore; the equation connecting the variables is;

c = 9b/a