Answer
$A=9$
Work Step by Step
The variation model described by the problem is $
A=kB
.$
Substituting the known values in the variation model above results to
\begin{array}{l}\require{cancel}
6=k(14)
\\
6=14k
\\
\dfrac{6}{14}=k
\\
\dfrac{\cancel2\cdot3}{\cancel2\cdot7}=k
\\
k=\dfrac{3}{7}
.\end{array}
Therefore, the variation equation is
\begin{array}{l}\require{cancel}
A=\dfrac{3}{7}B
.\end{array}
Using the variation equation above, then
\begin{array}{l}\require{cancel}
A=\dfrac{3}{7}(21)
\\
A=\dfrac{3}{\cancel7}(\cancel7\cdot3)
\\
A=9
.\end{array}
Hence, $
A=9
.$
