# 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} cups b. frac{2}{3} cup c. frac{3}{5} cup d. frac{1}{9} cup

Question
Equations and inequalities
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?
$$a. 1\frac{1}{2} cups$$
$$b. \frac{2}{3} cup$$
$$c. \frac{3}{5} cup$$
$$d. \frac{1}{9} cup$$

2021-02-17
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:
$$x/30=1/3/6$$
Solve for x:
$$x/30=1/18$$
Multiply both sides by 30:
$$(x/30)(30)=(1/18)(30)$$
$$x=5/3=1(2/3)$$ cups
So, the answer is choice A.

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