Question
A local book fair sells used books and new books. Braulio purchases three used books and one new book and spends $37.25
. Priyanka purchases three used books and five new books and spends $99.25
.
Complete the tape diagram that can be used to find the cost of one used book and one new book at the book fair.
Four rectangular bars arranged in a tape diagram.
A series of eight connected rectangular sections arranged in a linear sequence forming a tape diagram.
. Priyanka purchases three used books and five new books and spends $99.25
.
Complete the tape diagram that can be used to find the cost of one used book and one new book at the book fair.
Four rectangular bars arranged in a tape diagram.
A series of eight connected rectangular sections arranged in a linear sequence forming a tape diagram.
Answers
GPT-4o mini
To create a tape diagram that represents the costs of used books and new books as per Braulio's and Priyanka's purchases, we can define the cost of one used book as \( U \) and the cost of one new book as \( N \).
### Step 1: Define the Purchases
- **Braulio's Purchase**:
- 3 used books: \( 3U \)
- 1 new book: \( 1N \)
- Total cost: \( 3U + 1N = 37.25 \) (1)
- **Priyanka's Purchase**:
- 3 used books: \( 3U \)
- 5 new books: \( 5N \)
- Total cost: \( 3U + 5N = 99.25 \) (2)
### Step 2: Create the Tape Diagram
- For Braulio:
- The tape diagram can show three equal sections representing the three used books (each section is \( U \)) and one section representing the new book (which is \( N \)).
```
| U | U | U | N |
Total = 37.25
```
- For Priyanka:
- The tape diagram can similarly represent the three used books (each being \( U \)) and five equal sections for the five new books (each section being \( N \)).
```
| U | U | U | N | N | N | N | N |
Total = 99.25
```
### Step 3: Combine into a Visual Tape Diagram
You can visualize it as follows:
1. **Braulio's Section** for used and new books:
```
| U | U | U | N | --> Total = 37.25
```
2. **Priyanka's Section** for used and new books:
```
| U | U | U | N | N | N | N | N | --> Total = 99.25
```
Each section of the tape represents a unit price for either a used or new book. This combined view helps see the relationship between purchases of Braulio and Priyanka, allowing the cost per book to be solved as a system of equations.
### Conclusion
From the equations \( 3U + 1N = 37.25 \) and \( 3U + 5N = 99.25 \), you can solve for \( U \) and \( N \) to find the individual costs. The tape diagram visually represents how many of each type of book Braulio and Priyanka bought, aiding in understanding the problem and computing the costs.
### Step 1: Define the Purchases
- **Braulio's Purchase**:
- 3 used books: \( 3U \)
- 1 new book: \( 1N \)
- Total cost: \( 3U + 1N = 37.25 \) (1)
- **Priyanka's Purchase**:
- 3 used books: \( 3U \)
- 5 new books: \( 5N \)
- Total cost: \( 3U + 5N = 99.25 \) (2)
### Step 2: Create the Tape Diagram
- For Braulio:
- The tape diagram can show three equal sections representing the three used books (each section is \( U \)) and one section representing the new book (which is \( N \)).
```
| U | U | U | N |
Total = 37.25
```
- For Priyanka:
- The tape diagram can similarly represent the three used books (each being \( U \)) and five equal sections for the five new books (each section being \( N \)).
```
| U | U | U | N | N | N | N | N |
Total = 99.25
```
### Step 3: Combine into a Visual Tape Diagram
You can visualize it as follows:
1. **Braulio's Section** for used and new books:
```
| U | U | U | N | --> Total = 37.25
```
2. **Priyanka's Section** for used and new books:
```
| U | U | U | N | N | N | N | N | --> Total = 99.25
```
Each section of the tape represents a unit price for either a used or new book. This combined view helps see the relationship between purchases of Braulio and Priyanka, allowing the cost per book to be solved as a system of equations.
### Conclusion
From the equations \( 3U + 1N = 37.25 \) and \( 3U + 5N = 99.25 \), you can solve for \( U \) and \( N \) to find the individual costs. The tape diagram visually represents how many of each type of book Braulio and Priyanka bought, aiding in understanding the problem and computing the costs.