Recipe 2

Anna's making muffins! These ingredients make 12 muffins:
3/4 cup of flour
1/2 cup of sugar
1/4 teaspoon salt
1 cup of milk
1/3 teaspoon cinnamon
7 tablespoons butter
2 teaspoons baking powder
1 egg 2 tablespoons brown sugar
Anna has an 8-muffin tray. What fractions of ingredients should she use?

Correct answer:

f =  0.5 c
s =  0.3333 c
s₂ =  0.1667 tsp
m =  0.6667 c
c =  0.2222 tsp
b =  4.6667 tsp
p =  1.3333 tsp
e =  0.6667
s₃ =  1.3333 tsp

Step-by-step explanation:

$$\begin{gathered} m_1=12 \\ {m}_2=8 \\ k=\frac{m_2}{m_1}=\frac{8}{12}=\frac{2}{3}\doteq 0.6667 \\ f=\frac{3}{4}\cdot k=\frac{3}{4}\cdot \frac{2}{3}=\frac{3\cdot 2}{4\cdot 3}=\frac{6}{12}=\frac{1}{2}\text{c}=0.5\text{c} \end{gathered}$$

$s=\frac{1}{2}\cdot k=\frac{1}{2}\cdot \frac{2}{3}=\frac{1\cdot 2}{2\cdot 3}=\frac{2}{6}=\frac{1}{3}\text{c}=0.3333\text{c}$

$s_2=\frac{1}{4}\cdot k=\frac{1}{4}\cdot \frac{2}{3}=\frac{1\cdot 2}{4\cdot 3}=\frac{2}{12}=\frac{1}{6}\text{tsp}=0.1667\text{tsp}$

$m=1\cdot k=1\cdot \frac{2}{3}=\frac{1\cdot 2}{3}=\frac{2}{3}=\frac{2}{3}\text{c}=0.6667\text{c}$

$c=\frac{1}{3}\cdot k=\frac{1}{3}\cdot \frac{2}{3}=\frac{1\cdot 2}{3\cdot 3}=\frac{2}{9}=\frac{2}{9}\text{tsp}=0.2222\text{tsp}$

$b=7\cdot k=7\cdot \frac{2}{3}=\frac{7\cdot 2}{3}=\frac{14}{3}=\frac{14}{3}\text{tsp}=4.6667\text{tsp}$

$p=2\cdot k=2\cdot \frac{2}{3}=\frac{2\cdot 2}{3}=\frac{4}{3}=\frac{4}{3}\text{tsp}=1.3333\text{tsp}$

$e=1\cdot k=1\cdot \frac{2}{3}=\frac{1\cdot 2}{3}=\frac{2}{3}=0.6667$

$s_3=2\cdot k=2\cdot \frac{2}{3}=\frac{2\cdot 2}{3}=\frac{4}{3}=\frac{4}{3}\text{tsp}=1.3333\text{tsp}$

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