The quantity a varies directly with b and c and inversely with dThe quantity d is tripledWhich of the following must be true for the relationship to remain the same?

We have the next relation:

A = (b*d) / c

because we have direct variation with b and d, but inversely variation with c.

Now, if we have 3d instead of d, we have:

A' = (b * (3d)) / c

now, we want A' = A. If b, c, and d are the same in both equations, we have that:

3bd/c = b*d/c

this will only be true if b or/and d are equal to 0.

If d remains unchanged, and we can play with the other two variables we have:

3b'd/c' = bd/c

3b'/c' = b/c

from this we can took that: if c' = c, then b' = b/3, and if b = b', then c' = 3c.

Of course, there are other infinitely large possible combinations that are also a solution for this problem where neither b' = b or c' = c