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24 August, 15:02

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?

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  1. 24 August, 15:40
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    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
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