18. Higher Order Thinking Write an addition and subtraction problem and equation for the diagram. Then find the missing value.

Certainly! Let's work through an example to illustrate how to create addition and subtraction problems based on a diagram, write corresponding equations, and find the missing value. **Example Diagram Description:** Imagine a simple bar diagram showing the number of apples and oranges in two baskets: - **Basket A:** 5 apples and _ oranges. - **Basket B:** _ apples and 3 oranges. Suppose the total number of fruits in both baskets is 16. **Step 1: Define the Variables** Let's assign variables to the missing values: - Let \( x \) = number of oranges in Basket A. - Let \( y \) = number of apples in Basket B. **Step 2: Create Addition and Subtraction Problems** Based on the diagram description: 1. **Addition Problem:** - Total fruits in Basket A plus total fruits in Basket B equals 16. - So, \( (5 + x) + (y + 3) = 16 \). 2. **Subtraction Problem:** - If we know the total number of apples or oranges, we can create related subtraction problems. For this example, suppose the total number of apples is 9. - Number of apples in Basket A plus Basket B equals 9: \( 5 + y = 9 \). **Step 3: Write the Equations** From the addition problem: \[ 5 + x + y + 3 = 16 \] Combine like terms: \[ x + y + 8 = 16 \] Subtract 8 from both sides: \[ x + y = 8 \quad \text{(Equation 1)} \] From the subtraction problem: \[ 5 + y = 9 \] Subtract 5 from both sides: \[ y = 4 \quad \text{(Equation 2)} \] **Step 4: Solve for the Missing Values** Using Equation 2, we found \( y = 4 \). Now, substitute \( y = 4 \) into Equation 1: \[ x + 4 = 8 \] Subtract 4 from both sides: \[ x = 4 \] **Step 5: Interpret the Results** - **Basket A:** 5 apples and **4 oranges**. - **Basket B:** **4 apples** and 3 oranges. **Summary of the Problems and Solutions:** 1. **Addition Equation:** \[ (5 + x) + (y + 3) = 16 \] Solved to find: \[ x = 4 \] (oranges in Basket A) \[ y = 4 \] (apples in Basket B) 2. **Subtraction Equation:** \[ 5 + y = 9 \] Solved to find: \[ y = 4 \] (apples in Basket B) **Conclusion:** By defining variables for the missing values, creating corresponding addition and subtraction equations based on the diagram, and solving the equations, we successfully found the missing quantities in the diagram.