# 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

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?
$a.1\frac{1}{2}\cup s$
$b.\frac{2}{3}\cup$
$c.\frac{3}{5}\cup$
$d.\frac{1}{9}\cup$

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Dora
Let x be the amount of sugar, in cups needed to make $2\frac{1}{2}$ dozen or 30 cupcakes. Using the ratio sugar/cupcake, we write the proportion:
$\frac{x}{30}=\frac{1}{3}/6$
Solve for x:
$\frac{x}{30}=\frac{1}{18}$
Multiply both sides by 30:
$\left(\frac{x}{30}\right)\left(30\right)=\left(\frac{1}{18}\right)\left(30\right)$
$x=\frac{5}{3}=1\left(\frac{2}{3}\right)$ cups
So, the answer is choice A.
Jeffrey Jordon