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#
a is inversely proportional to (b - 4). If a = 8 and b = 22, express a in terms of b.

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Question:

A
\(a= \frac{\mathrm{144} }{\mathrm{(b-4)}}\)

explanation

A value (given as a in this problem) that is inversely proportional to another value (given as b-4) is written as (where k is a constant of proportionality): \(a= \frac{\mathrm{k} }{\mathrm{(b-4)}}\)

substituting with given values of a and b: \(8=\frac{\mathrm{k} }{\mathrm{(22-4)}} \)

\(8(22−4)=k\)

\(k=144\)

\(a= \frac{\mathrm{144} }{\mathrm{(b-4)}}\)

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