Question

Grandma Betty's recipe makes 6 cupcakes and uses \(\frac{1}{3}\) of a cup of sugar. How many cups of sugar will it take to make 2 \(\frac{1}{2}\) dozen cupcakes?
\(\displaystyle{a}.{1}{\frac{{{1}}}{{{2}}}}\cup{s}\)
\(\displaystyle{b}.{\frac{{{2}}}{{{3}}}}\cup\)
\(\displaystyle{c}.{\frac{{{3}}}{{{5}}}}\cup\)
\(\displaystyle{d}.{\frac{{{1}}}{{{9}}}}\cup\)

Answer 1

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.