Answer :
To solve this problem, you'll want to figure out how much milk is needed when scaling the recipe up from 2/3 cup of potatoes to 2 cups of potatoes.
First, let's understand the original ratio given in the recipe. The recipe calls for [tex]\frac{2}{3}[/tex] cup of potatoes for every [tex]\frac{1}{3}[/tex] cup of milk. This means for every 2 parts of potatoes, you need 1 part of milk.
Now, you have 2 cups of potatoes. To find out how much milk you need, you can set up a proportion based on the given ratio:
Start with the original ratio of potatoes to milk: [tex]\frac{2}{3} \text{ cups of potatoes} : \frac{1}{3} \text{ cup of milk}[/tex]
You want to find out how much milk is needed for 2 cups of potatoes. Set up the proportion: [tex]\frac{2}{3} : \frac{1}{3} = 2 : x[/tex] where [tex]x[/tex] is the amount of milk needed.
Solve the proportion to find [tex]x[/tex]:
- Cross-multiply to get: [tex]2 \times \frac{1}{3} = x \times \frac{2}{3}[/tex]
- Simplify each side: [tex]\frac{2}{3} = \frac{2}{3}x[/tex]
- Divide both sides by [tex]\frac{2}{3}[/tex] to isolate [tex]x[/tex]:
[tex]x = \frac{\frac{2}{3}}{\frac{2}{3}}[/tex] - This simplifies to: [tex]x = 1[/tex]
Therefore, you will need 1 cup of milk for 2 cups of potatoes to maintain the same ratio as the original recipe.