Let x be the amount of sugar, in cups needed to make \(\displaystyle{2}{\frac{{{1}}}{{{2}}}}\) dozen or 30 cupcakes. Using the ratio sugar/cupcake, we write the proportion:

\(\displaystyle\frac{{x}}{{30}}=\frac{{1}}{{3}}/{6}\)

Solve for x:

\(\displaystyle\frac{{x}}{{30}}=\frac{{1}}{{18}}\)

Multiply both sides by 30:

\(\displaystyle{\left(\frac{{x}}{{30}}\right)}{\left({30}\right)}={\left(\frac{{1}}{{18}}\right)}{\left({30}\right)}\)

\(\displaystyle{x}=\frac{{5}}{{3}}={1}{\left(\frac{{2}}{{3}}\right)}\) cups

So, the answer is choice A.

\(\displaystyle\frac{{x}}{{30}}=\frac{{1}}{{3}}/{6}\)

Solve for x:

\(\displaystyle\frac{{x}}{{30}}=\frac{{1}}{{18}}\)

Multiply both sides by 30:

\(\displaystyle{\left(\frac{{x}}{{30}}\right)}{\left({30}\right)}={\left(\frac{{1}}{{18}}\right)}{\left({30}\right)}\)

\(\displaystyle{x}=\frac{{5}}{{3}}={1}{\left(\frac{{2}}{{3}}\right)}\) cups

So, the answer is choice A.