2. Read the story situation: A total of 987 aluminum cans, plastic bottles, and glass bottles were recycled last month. Four hundred nine glass bottles were recycled. One hundred fourteen fewer plastic bottles were recycled than glass bottles. How many aluminum cans were recycled? a. Draw a bar model to represent the story situation.

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UpStudy AI · Accepted Answer

To create a **bar model** for the given story situation, follow these steps:

### **1. Understand the Components:**
- **Total Recycled Items:** 987 (Aluminum cans + Plastic bottles + Glass bottles)
- **Glass Bottles Recycled:** 409
- **Plastic Bottles Recycled:** 114 fewer than glass bottles

### **2. Visual Representation:**

Here's how you can draw the bar model:

```
+---------------------------+---------------------------+---------------------------+
|       Aluminum Cans       |       Plastic Bottles     |        Glass Bottles      |
|                           |       (409 - 114) = 295   |           409             |
+---------------------------+---------------------------+---------------------------+
|                                   Total: 987                                     |
+-------------------------------------------------------------------+
```

### **3. Description of the Bar Model:**

- **Total Bar:** Represents the **total** number of recycled items (987).
  
- **Breakdown into Three Sections:**
  - **Aluminum Cans:** This section will represent the unknown number of aluminum cans recycled.
  - **Plastic Bottles:** This section is labeled as **295** (since it's 114 fewer than the 409 glass bottles).
  - **Glass Bottles:** This section is labeled as **409**.

### **4. Step-by-Step Breakdown:**

1. **Start with the Total:** Draw a large rectangle divided into three parts horizontally or vertically.
2. **Label Each Section:**
   - **Glass Bottles:** Assign the value **409**.
   - **Plastic Bottles:** Since there are **114 fewer** than glass bottles, calculate **409 - 114 = 295** and assign this value.
   - **Aluminum Cans:** Leave this section blank for now as it's the unknown we need to find.
3. **Ensure the Sum Equals Total:** The sum of all three sections should equal **987**.

### **Visual Aid:**

While I can't draw the bar model here, envision it as three adjacent rectangles within a larger rectangle:

```
+---------------+---------------+---------------+
| Aluminum Cans | Plastic Bottles| Glass Bottles|
|               |      295      |      409      |
+---------------+---------------+---------------+
|             Total = 987                    |
+-------------------------------------------+
```

This bar model helps visualize how the total number of recycled items is distributed among aluminum cans, plastic bottles, and glass bottles.

To find the number of **Aluminum Cans** recycled, you would subtract the sum of plastic and glass bottles from the total:

$$ \text{Aluminum Cans} = 987 - (295 + 409) = 987 - 704 = 283 $$

So, **283 aluminum cans** were recycled.
283 aluminum cans were recycled.

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