Question

a recipe calls for 1/2 cup 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?

Answer 1

(1/2) / (1 + 2/3) = (4) / (B ) simplify (1/2) / ( 5/3) = 4 /(B) cross-multiply B(1/2) = (5/3)(4) B(1/2) = 20/3 multiply both sides by 2 B = 40/3 cups of B = 13 + 1/3 cups of B

Answer 2

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  $=13\frac{1}{3}$