Cups of ingredient b needed \(=13\frac{1}{3}\)
Step-by-step explanation:
A recipe calls for 1/2 cup ingredient a for every 1 2/3 cups of ingredient b.
\(\texttt{Ratio of ingredient a : Ratio of ingredient b = }\frac{1}{2}:1\frac{2}{3}\\\\\texttt{Ratio of ingredient a : Ratio of ingredient b = }\frac{1}{2}:\frac{1\times 3+2}{3}\\\\\texttt{Ratio of ingredient a : Ratio of ingredient b = }\frac{1}{2}:\frac{5}{3}\)
Let us assume ingredient of b needed is b.
We have
\(4:b= \frac{1}{2}:\frac{5}{3}\\\\\frac{4}{b}=\frac{\frac{1}{2}}{\frac{5}{3}}\\\\\frac{4}{b}=\frac{3}{10}\\\\b=\frac{40}{3}=\frac{39+1}{3}=13\frac{1}{3}\)
Cups of ingredient b needed \(=13\frac{1}{3}\)
