+14 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?
+2446 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. |
