- The relationship is defined as 3 cups of milk for 4 tablespoons of chocolate powder.
- We set up a proportion to find the unit rate: \(\frac{4 \text{ tablespoons}}{3 \text{ cups}} = \frac{x \text{ tablespoons}}{1 \text{ cup}}\).
- Solving for \(x\) gives the unit rate of \(\frac{4}{3}\) tablespoons of chocolate powder per cup of milk.
- Final Answer: \(\boxed{\frac{4}{3}}\).
Explanation
- Analyzing the Problem
We are given that Mixture X uses 3 cups of milk for 4 tablespoons of chocolate powder. We want to find the unit rate, which represents the number of tablespoons of chocolate powder required for 1 cup of milk. The data provided is:
- Milk: 3 cups
- Chocolate powder: 4 tablespoons
We need to find the value corresponding to 1 cup of milk in the provided table.
- Calculating the Unit Rate
To find the unit rate of tablespoons per cup, we set up the ratio of chocolate powder to milk. We have 4 tablespoons of chocolate powder for 3 cups of milk. Let \(x\) be the amount of chocolate powder for 1 cup of milk. We can express this relationship as a proportion:
\[\frac{\text{Chocolate Powder}}{\text{Milk}} = \frac{4 \text{ tablespoons}}{3 \text{ cups}} = \frac{x \text{ tablespoons}}{1 \text{ cup}}\]
To solve for \(x\), we divide the number of tablespoons by the number of cups:
\[x = \frac{4}{3}\]
Thus, for 1 cup of milk, there are \(\frac{4}{3}\) tablespoons of chocolate powder.
- Conclusion
The unit rate is \(\frac{4}{3}\) tablespoons of chocolate powder per cup of milk. This can be expressed as a fraction or as a mixed number: \(\frac{4}{3} = 1\frac{1}{3}\). Therefore, there are \(\frac{4}{3}\) tablespoons of chocolate powder for 1 cup of milk. The final answer is \(\boxed{\frac{4}{3}}\).
Examples
Unit rates are extremely useful in everyday life, especially in cooking and grocery shopping. For example, if you know that a recipe requires 3 cups of milk for 4 tablespoons of chocolate powder, understanding the unit rate of \(\frac{4}{3}\) tablespoons per cup allows you to easily scale the recipe. Whether you only have 1 cup of milk or need to make a massive batch with 10 cups, knowing the amount per single unit makes adjusting your ingredients simple and efficient. This concept is the foundation of proportional reasoning in real-world applications.