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For a blueberry recipe, you need 3/4 cups of sugar, 1/8 cup of butter and 3/8 cup of blueberry. How many cups of sugar AND butter are needed if a single cup of blueberries is used in this mix?

 May 23, 2017
 #1
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2 cups of sugar

1/3 cups of butter

 

Setup proportions to solve for both the sugar and butter. In a recipe, all ingredients must be proportional because otherwise, the meal will be not be exactly as the recipe calls for:

 

Let x = the cups of sugar

Let y = the cups of butter

 

\(\frac{\frac{3}{4}}{x}=\frac{\frac{3}{8}}{1}=\frac{\frac{1}{8}}{y}\)

 

We should solve each proportional individually. I'll solve for the cups of sugar first:

 

\(\frac{\frac{3}{4}}{x}=\frac{\frac{3}{8}}{1}\) Solve by cross multiplying
\(\frac{3}{4}=\frac{3}{8}x\) Multiply by 8/3 on both sides to isolate x
\(x=\frac{3}{4}*\frac{8}{3}\) Simplify the right hand side
\(x=\frac{24}{12}=2\)cups of sugar! I multiplied the fraction and then reduced it to simplest terms.
   

 

Let's utilize the exact same process for solving for y, the amount of cups of butter:

 

\(\frac{\frac{3}{8}}{1}=\frac{\frac{1}{8}}{y}\) Cross muliply and solve for y
\(\frac{3}{8}y=\frac{1}{8}\) Multiply by 8/3 on both sides
\(y=\frac{1}{8}*\frac{8}{3}\) Simplify the right hand side
\(y=\frac{8}{24}=\frac{1}{3}\) cups of butter! I multiplied the fraction and reduced it to simplest terms.
   
 May 23, 2017
edited by TheXSquaredFactor  May 23, 2017

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