The variable a varies jointly with b and c. We can assume there is a constant of proportionality between a and b and c as:
[tex]a=k\cdot b\cdot c[/tex]We know that when b=2/3 and c=1/6, a is equal to 14. Then we can calculate k as:
[tex]\begin{gathered} a=k\cdot b\cdot c \\ 14=k\cdot\frac{2}{3}\cdot\frac{1}{6} \\ 14=k\cdot\frac{2}{18} \\ k=14\cdot\frac{18}{2} \\ k=126 \end{gathered}[/tex]Then, when b=1/9 and c=1/2 we will get:
[tex]\begin{gathered} a=126\cdot b\cdot c \\ a=126\cdot\frac{1}{9}\cdot\frac{1}{2} \\ a=\frac{126}{18} \\ a=7 \end{gathered}[/tex]Answer: a = 7 [option D]
