Respuesta :
Answer:
[tex]13\frac{1}{3}[/tex] cups
Step-by-step 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.
[tex]1\frac{2}{3}=\frac{5}{3}[/tex]
[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{\frac{1}{2}}{\frac{5}{3}}[/tex]
[tex]\frac{\text{Number of cups of ingredient A}}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]
Now let us substitute our amount of Ingredient A =4 in our proportions.
[tex]\frac{4}{\text{Number of cups of ingredient B}} =\frac{3}{10}[/tex]
[tex]\frac{\text{Number of cups of ingredient B}}{4}=\frac{10}{3}[/tex]
Multiplying both sides of our equation by 4.
[tex]4*\frac{\text{Number of cups of ingredient B}}{4}=4*\frac{10}{3}[/tex]
[tex]\text{Number of cups of ingredient B}=\frac{40}{3}[/tex]
[tex]\text{Number of cups of ingredient B}=13\frac{1}{3}[/tex]
Therefore, we need [tex]13\frac{1}{3}[/tex] cups of ingredient B to make our recipe.
Answer:
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;
[tex]\frac{\frac{1}{2} }{1\frac{2}{3} } = \frac{4}{B}[/tex]
Simplify:
[tex]\frac{\frac{1}{2} }{\frac{5}{3}} = \frac{4}{B}[/tex]
By cross multiply we get;
[tex]B \cdot \frac{1}{2} = 4 \cdot \frac{5}{3}[/tex]
or
[tex]\frac{B}{2} = \frac{20}{3}[/tex]
Multiply both sides by 2 we get;
[tex]B = \frac{20}{3} \times 2 = \frac{40}{3} = 13\frac{1}{3}[/tex]
Therefore, [tex]13\frac{1}{3}[/tex] cups of ingredients B needs.
