Problem 95 - Algebra A Combined Function

Question

The chart shows the average number of pounds of various dairy products consumed by each U.S. citizen. Use this chart for Exercises 95 and 96. (Source: Dairy Information Center) $$ \begin{array}{|c|c|} \hline \text { Dairy Product } & \text { Pounds } \\ \hline \text { Fluid Milk } & 213.4 \\ \hline \text { Cheese } & 30.8 \\ \hline \text { Butter } & 4.4 \\ \hline \end{array} $$ How much more fluid milk products than cheese products does the average U.S. citizen consume?

Step-by-Step Solution

Answer

182.6 pounds more fluid milk than cheese is consumed by the average U.S. citizen.

Step 1: Identify Quantities

From the table, the average U.S. citizen consumes 213.4 pounds of fluid milk and 30.8 pounds of cheese.

Step 2: Set Up the Calculation

To find out how much more fluid milk is consumed than cheese, we need to subtract the amount of cheese from the amount of fluid milk.

Step 3: Perform the Subtraction

Calculate the difference: \[ 213.4 - 30.8 = 182.6 \]

Step 4: Interpret the Result

The calculation shows that the average U.S. citizen consumes 182.6 more pounds of fluid milk than cheese.

Key Concepts

Data Interpretation

Understanding how to interpret data from a chart is crucial for solving real-world problems in algebra. In our exercise, we were provided with a table showing the average number of pounds of various dairy products consumed by each U.S. citizen. These types of tables allow us to easily compare numerical values across different categories.

Here are a few steps to help with data interpretation:

• Identify the Variables: Look at what is being measured, in this case, the types of dairy products and their respective average consumption.


• Understand the Context: Recognize that the numbers represent averages for U.S. citizens, providing a broad overview of consumption patterns.


• Determine the Task: Identify what you need to find or accomplish with the data. For instance, the exercise asks us to find the difference in consumption between fluid milk and cheese.

By breaking the problem into these steps, students can enhance their ability to extract key information from data presentations, which is an invaluable skill in both academic and practical settings.

Subtraction

Subtraction is a fundamental arithmetic operation in algebra that helps us find the difference between two values. In our specific problem, we are using subtraction to determine how many more pounds of milk were consumed compared to cheese.

Let's explore subtraction with an easy example:

• Initial Value: Begin with an initial amount, like 213.4 pounds of fluid milk.


• Subtraction Value: Subtract the quantity representing another amount, here 30.8 pounds representing cheese consumption.


• Solution: Perform the operation: subtract the smaller number from the larger number, ensuring proper alignment of decimal points.

Through this subtraction, we find that approximately 182.6 more pounds of fluid milk are consumed compared to cheese among U.S. citizens. Mastering subtraction in its basic form lays the groundwork for more complex algebraic operations.

Step-by-step Solution

A step-by-step solution provides a clear roadmap of the logical sequence used to solve a problem. This approach helps in understanding not just the answer but the process of obtaining it.

The key steps to follow include:

• Identify the Data: Clearly note the specific figures involved from the data set, like 213.4 pounds of milk and 30.8 pounds of cheese.


• Set Up the Equation: Knowing the algebraic operation needed, set up the calculation: in this case, the subtraction of two numbers.


• Execute the Calculation: Perform the necessary arithmetic accurately to get to the solution, ensuring all steps are followed in order.


• Draw Conclusions: Interpret the result, which enlightens us that the difference computed reflects the extra consumption of fluid milk.

Using a step-by-step breakdown ensures that each component of the process is understandable, reinforcing how to approach algebraic problems systematically.