Answer
9 T-shirts cost R1,080.
Total Cost: R1,080
Solution
Certainly! Let's solve the problem of determining the total cost of 9 T-shirts, each costing R120, using **three different methods**. We'll also visualize the relationship between the number of T-shirts and the total cost with a graph.
---
### **Problem Statement**
**T-shirts cost R120 each. How much will 9 T-shirts cost?**
---
### **Method 1: Repeated Addition**
In this method, we add the cost of one T-shirt repeatedly until we reach the desired quantity.
\[
\begin{array}{l}
\text{Cost of 1 T-shirt} = R120 \\
\text{Cost of 9 T-shirts} = R120 + R120 + R120 + R120 + R120 + R120 + R120 + R120 + R120 \\
= 9 \times R120 \\
= R1,\!080 \\
\end{array}
\]
**Total Cost:** R1,080
---
### **Method 2: Multiplication**
Multiplication is a quicker way to calculate the total cost when dealing with equal quantities.
\[
\begin{array}{l}
\text{Cost per T-shirt} = R120 \\
\text{Number of T-shirts} = 9 \\
\text{Total Cost} = \text{Cost per T-shirt} \times \text{Number of T-shirts} \\
= R120 \times 9 \\
= R1,\!080 \\
\end{array}
\]
**Total Cost:** R1,080
---
### **Method 3: Using a Graph**
We can visualize the relationship between the number of T-shirts and the total cost with a graph. This method helps in understanding how the total cost increases with each additional T-shirt.
#### **Step-by-Step Process:**
1. **Define Variables:**
- Let **\( x \)** represent the number of T-shirts.
- Let **\( y \)** represent the total cost in Rands.
2. **Establish the Relationship:**
- The total cost \( y \) is directly proportional to the number of T-shirts \( x \).
- This can be expressed as: \( y = 120x \)
3. **Plot the Graph:**
- **X-axis (Horizontal):** Number of T-shirts (\( x \))
- **Y-axis (Vertical):** Total Cost in Rands (\( y \))
- **Slope:** 120 (since each additional T-shirt adds R120 to the total cost)
- **Intercept:** 0 (if you buy 0 T-shirts, the cost is R0)
4. **Plotting the Point for 9 T-shirts:**
- When \( x = 9 \): \( y = 120 \times 9 = 1,\!080 \)
- This point (9, 1,080) lies on the line.
#### **Graph Illustration:**
```plaintext
Total Cost (R) |
|
1200 + |
| *
1080 + |--------------------- (9, 1080)
|
960 + |
|
840 + |
|
720 + |
|
600 + |
|
480 + |
|
360 + |
|
240 + |
|
120 + |
|
0 +----+----+----+----+----+----+----+----+----+
0 1 2 3 4 5 6 7 8 9
Number of T-shirts
```
**Explanation of the Graph:**
- The graph is a straight line starting from the origin (0,0), indicating that if you buy 0 T-shirts, the cost is R0.
- The slope of the line is 120, meaning each additional T-shirt increases the total cost by R120.
- The point (9, 1,080) is plotted to show that 9 T-shirts cost R1,080.
---
### **Summary of Solutions**
| Method | Calculation | Total Cost |
|----------------|-----------------------------------------------|------------|
| **Method 1:** Repeated Addition | R120 + R120 + ... (9 times) | R1,080 |
| **Method 2:** Multiplication | R120 × 9 | R1,080 |
| **Method 3:** Graphical Representation | See the graph above | R1,080 |
All three methods consistently show that **9 T-shirts cost R1,080**.
---
### **Conclusion**
Using different methods—**repeated addition**, **multiplication**, and a **graphical representation**—we've determined that purchasing 9 T-shirts at R120 each results in a total cost of **R1,080**. This demonstrates the consistency and reliability of various mathematical approaches to solving the same problem.
Reviewed and approved by the UpStudy tutoring team
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