A recipe 3

A recipe calls for 1/2 cup of ingredient A for every 1 2/3 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?

Correct answer:

B =  13 ¹⁄₃ = 40/3

Step-by-step explanation:

$$\begin{gathered} A=4 \\ a=\frac{1}{2}=0.5 \\ b=1\frac{2}{3}=1+\frac{2}{3}=\frac{1\cdot 3+2}{3}=\frac{3+2}{3}=\frac{5}{3}=1\frac{2}{3}\doteq 1.6667 \\ r=b/a=\frac{5}{3}/\frac{1}{2}=\frac{5}{3}:\frac{1}{2}=\frac{5}{3}\cdot \frac{2}{1}=\frac{5\cdot 2}{3\cdot 1}=\frac{10}{3}\doteq 3.3333 \\ B=A\cdot r=4\cdot \frac{10}{3}=\frac{4\cdot 10}{3}=\frac{40}{3}=13\frac{1}{3}=13.3333 \end{gathered}$$

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