Question

A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you? need?

Answer 1

Proportion states that the two ratios are equal.

Given statement: A recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B. You use 4 cups of ingredient A.

By using proportion definition to find ingredients B;

`((1)/(2) )/(1(2)/(3) ) = (4)/(B)`

Simplify:

`((1)/(2) )/((5)/(3)) = (4)/(B)`

By cross multiply we get;

`B \cdot (1)/(2) = 4 \cdot (5)/(3)`

or

`(B)/(2) = (20)/(3)`

Multiply both sides by 2 we get;

`B = (20)/(3) * 2 = (40)/(3) = 13(1)/(3)`

Therefore,
`13(1)/(3)` cups of ingredients B needs.

Answer 2

`13(1)/(3)` cups

Explanation:

We are told that a recipe calls for one half cup of ingredient A for every 1 and two thirds cups of ingredient B.

To find the number of cups of ingredient B we will use proportions.

`1(2)/(3)=(5)/(3)`

`\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =((1)/(2))/((5)/(3))`

`\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =(3)/(10)`

Now let us substitute our amount of Ingredient A =4 in our proportions.

`\frac{4}{\text{Number of cups of ingredient B}} =(3)/(10)`

`\frac{\text{Number of cups of ingredient B}}{4}=(10)/(3)`

Multiplying both sides of our equation by 4.

`4*\frac{\text{Number of cups of ingredient B}}{4}=4*(10)/(3)`

`\text{Number of cups of ingredient B}=(40)/(3)`

`\text{Number of cups of ingredient B}=13(1)/(3)`

Therefore, we need
`13(1)/(3)` cups of ingredient B to make our recipe.