A pancake

A pancake recipe requires 1 2/3 cups of flour to make 20 pancakes, and you have 9 cups of flour. How many pancakes can you make with 1 cup of flour? How many pancakes can you make with 9 cups of flour?

Correct answer:

n₁ =  12
n₉ =  108

Step-by-step explanation:

$$\begin{gathered} m_{20}=1\frac{2}{3}=1+\frac{2}{3}=\frac{1\cdot 3+2}{3}=\frac{3+2}{3}=\frac{5}{3}=1\frac{2}{3}\doteq 1.6667\text{c} \\ {m}_1=m_{20}/20=\frac{5}{3}/20=\frac{5}{3\cdot 20}=\frac{5}{60}=\frac{1}{12}\doteq 0.0833\text{c} \\ {M}_1=1\text{c} \\ {n}_1=M_1/m_1=1/\frac{1}{12}=1:\frac{1}{12}=1\cdot \frac{12}{1}=\frac{1\cdot 12}{1}=\frac{12}{1}=12 \end{gathered}$$

$$\begin{gathered} M_9=9\text{c} \\ {n}_9=M_9/m_1=9/\frac{1}{12}=9:\frac{1}{12}=9\cdot \frac{12}{1}=\frac{9\cdot 12}{1}=\frac{108}{1}=108 \end{gathered}$$

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