# Math Help - [SOLVED] Complex Proportions

1. ## [SOLVED] Complex Proportions

M is jointly proportional to a, b, and c and inversely proportional to d. If a and d have the same value and if b and c are both 2, then M=128.
Express the statement as a formula. Use the given information to find the constant of proportionality. k=?

2. You must get the magic words in your head.

Directly Proportional ==> kx

Inversely Proportional ==> k/x

"M is jointly proportional to a, b, and c and inversely proportional to d."

M = k(abc)/d

Really, that's all there is to translating these. The rest is a substitution exercise.

"a = d"

M = k(abc)/a = k(bc)(a/a) = kbc

"b and c are both 2"

M = kbc = k(2)(2) = 4k

"M = 128"

M = 4k = 128

You should be able to solve that for 'k'.