Set 4 Interpret Algebraic Expressions in Real-World Problems Identify and interpret the parts of each expression. 1) A pen costs $$ \$ 2.50 $$. The expression $$ 4 n+2.50 $$ represents the cost of buying 4 notebooks and a pen. What is the product in the expression? What does the product represent? 2) Henry has 50 apples. He gives 4 apples each to $$ f $$ friends. What is the difference in the expression $$ 50-4 f $$ ? What does the difference represent? 3) The number of roses and daisies in 5 bouquets is $$ 5(r+d) $$. What is the sum in the expression? What does the sum represent?

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Let's analyze each problem step-by-step to identify and interpret the specified parts of the algebraic expressions.

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### **1) Cost of 4 Notebooks and a Pen**

**Given:**
- **Cost of a pen:** \$2.50
- **Expression:** $$ 4n + 2.50 $$
  
**Questions:**
- **What is the product in the expression?**
- **What does the product represent?**

**Analysis:**
- **Product Identification:**
  - In the expression $$ 4n + 2.50 $$, the term $$ 4n $$ is the product.
  - **Product:** $$ 4n $$
  
- **Interpretation of the Product:**
  - Here, $$ n $$ represents the cost of one notebook.
  - Multiplying $$ n $$ by 4 ($$ 4n $$) gives the total cost for **4 notebooks**.
  
**Summary:**
- **Product:** $$ 4n $$
- **Represents:** The total cost of purchasing **4 notebooks**.

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### **2) Henry's Apples Distribution**

**Given:**
- **Total apples Henry has:** 50
- **Apples given to each friend:** 4
- **Expression:** $$ 50 - 4f $$
  
**Questions:**
- **What is the difference in the expression?**
- **What does the difference represent?**

**Analysis:**
- **Difference Identification:**
  - In the expression $$ 50 - 4f $$, the entire expression represents the **difference**.
  - **Difference:** $$ 50 - 4f $$
  
- **Interpretation of the Difference:**
  - $$ f $$ stands for the number of friends.
  - $$ 4f $$ calculates the total number of apples given away ($$ 4 $$ apples to each of $$ f $$ friends).
  - Subtracting $$ 4f $$ from 50 ($$ 50 - 4f $$) gives the **remaining apples** Henry has after distributing.

**Summary:**
- **Difference:** $$ 50 - 4f $$
- **Represents:** The number of **apples remaining** after Henry gives **4 apples to each of $$ f $$ friends**.

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### **3) Number of Roses and Daisies in Bouquets**

**Given:**
- **Number of bouquets:** 5
- **Expression:** $$ 5(r + d) $$
  
**Questions:**
- **What is the sum in the expression?**
- **What does the sum represent?**

**Analysis:**
- **Sum Identification:**
  - Inside the parentheses $$ (r + d) $$ is the **sum**.
  - **Sum:** $$ r + d $$
  
- **Interpretation of the Sum:**
  - $$ r $$ represents the number of roses in one bouquet.
  - $$ d $$ represents the number of daisies in one bouquet.
  - Adding them together ($$ r + d $$) gives the **total number of flowers per bouquet**.

- The entire expression $$ 5(r + d) $$ then calculates the total number of roses and daisies in **5 bouquets**.

**Summary:**
- **Sum:** $$ r + d $$
- **Represents:** The **total number of roses and daisies in **one bouquet**.

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By breaking down each expression, we've identified the specific parts (product, difference, sum) and interpreted their real-world meanings within the given contexts.
- **1) Product:** $$ 4n $$ represents the total cost of 4 notebooks. - **2) Difference:** $$ 50 - 4f $$ represents the remaining apples after giving 4 to each friend. - **3) Sum:** $$ r + d $$ represents the total number of roses and daisies in one bouquet.

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