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

Cups of ingredient b needed
`=13(1)/(3)`

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 = }(1)/(2):1(2)/(3)\\\\\texttt{Ratio of ingredient a : Ratio of ingredient b = }(1)/(2):(1* 3+2)/(3)\\\\\texttt{Ratio of ingredient a : Ratio of ingredient b = }(1)/(2):(5)/(3)`

Let us assume ingredient of b needed is b.

We have

`4:b= (1)/(2):(5)/(3)\\\\(4)/(b)=((1)/(2))/((5)/(3))\\\\(4)/(b)=(3)/(10)\\\\b=(40)/(3)=(39+1)/(3)=13(1)/(3)`

Cups of ingredient b needed
`=13(1)/(3)`