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?a. 1frac{1}{2} cupsb. frac{2}{3} cupc. frac{3}{5} cupd. frac{1}{9} cup

Equations and inequalities
ANSWERED 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?
$$\displaystyle{a}.{1}{\frac{{{1}}}{{{2}}}}\cup{s}$$
$$\displaystyle{b}.{\frac{{{2}}}{{{3}}}}\cup$$
$$\displaystyle{c}.{\frac{{{3}}}{{{5}}}}\cup$$
$$\displaystyle{d}.{\frac{{{1}}}{{{9}}}}\cup$$ 2021-01-20
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.