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 a 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:

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

$s={\displaystyle \frac{1}{2}}\cdot k={\displaystyle \frac{1}{2}}\cdot 0.6667={\displaystyle \frac{1}{3}}\text{ c}=0.3333\text{ c}$

$s_2={\displaystyle \frac{1}{4}}\cdot k={\displaystyle \frac{1}{4}}\cdot 0.6667={\displaystyle \frac{1}{6}}\text{ tsp}=0.1667\text{ tsp}$

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

$c={\displaystyle \frac{1}{3}}\cdot k={\displaystyle \frac{1}{3}}\cdot 0.6667={\displaystyle \frac{2}{9}}\text{ tsp}=0.2222\text{ tsp}$

$b=7\cdot k=7\cdot 0.6667={\displaystyle \frac{14}{3}}\text{ tsp}=4.6667\text{ tsp}$

$p=2\cdot k=2\cdot 0.6667={\displaystyle \frac{4}{3}}\text{ tsp}=1.3333\text{ tsp}$

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

$s_3=2\cdot k=2\cdot 0.6667={\displaystyle \frac{4}{3}}\text{ tsp}=1.3333\text{ tsp}$

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