Question
eith and Reina are buying school supplies for the upcoming school year. Keith buys four notebooks and three packs of pens and spends 36.80
. Reina buys four notebooks and one pack of pens and spends 21.60
.
PART A
Drag the tiles to create a tape diagram that could be used to find the cost of one set of calculators and one pack of markers.
Use the
tile for notebooks and the
tile for packs of pens.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A rectangular tile with "36.8 =" in the center.
A rectangular tile with "21.6 =" in the center.
Question 2
PART B
What is the cost of one notebook, and what is the cost of one pack of pens?
One notebook:
One pack of pens:
. Reina buys four notebooks and one pack of pens and spends 21.60
.
PART A
Drag the tiles to create a tape diagram that could be used to find the cost of one set of calculators and one pack of markers.
Use the
tile for notebooks and the
tile for packs of pens.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A rectangular tile with "36.8 =" in the center.
A rectangular tile with "21.6 =" in the center.
Question 2
PART B
What is the cost of one notebook, and what is the cost of one pack of pens?
One notebook:
One pack of pens:
Answers
GPT-4o mini
Let's break down how we can solve this problem step by step.
### PART A: Tape Diagram Setup
To create a tape diagram based on Keith and Reina's purchases, we can represent each expenditure:
- **Keith's purchase** consists of 4 notebooks and 3 packs of pens for a total cost of 36.80.
- **Reina's purchase** consists of 4 notebooks and 1 pack of pens for a total cost of 21.60.
We can set up the tape diagram as follows:
1. Use one rectangular tile labeled "36.8 =" to represent the total cost of Keith's purchase.
2. Below it, draw another rectangular tile labeled "21.6 =" to represent the total cost of Reina's purchase.
3. For both diagrams, you can represent each notebook with a tile labeled "N" and each pack of pens with a tile labeled "P."
The resulting tape diagrams can be named like this:
- Keith's purchase: 4N + 3P = 36.80
- Reina's purchase: 4N + 1P = 21.60
### PART B: Cost of One Notebook and One Pack of Pens
To find the cost of one notebook and one pack of pens, we will set up the following equations based on the information provided:
1. From Keith's purchase:
\[
4N + 3P = 36.80 \quad \text{(1)}
\]
2. From Reina's purchase:
\[
4N + 1P = 21.60 \quad \text{(2)}
\]
Now we can solve these equations.
**Step 1: Subtract equation (2) from equation (1)**:
\[
(4N + 3P) - (4N + 1P) = 36.80 - 21.60
\]
This simplifies to:
\[
2P = 15.20
\]
Dividing both sides by 2 gives:
\[
P = 7.60
\]
**Step 2: Substitute P back into one of the original equations to find N. I will use equation (2) for that**:
\[
4N + 1(7.60) = 21.60
\]
This simplifies to:
\[
4N + 7.60 = 21.60
\]
Subtracting 7.60 from both sides gives:
\[
4N = 14.00
\]
Dividing both sides by 4 gives:
\[
N = 3.50
\]
### Final Answers
- One notebook: **3.50**
- One pack of pens: **7.60**
### PART A: Tape Diagram Setup
To create a tape diagram based on Keith and Reina's purchases, we can represent each expenditure:
- **Keith's purchase** consists of 4 notebooks and 3 packs of pens for a total cost of 36.80.
- **Reina's purchase** consists of 4 notebooks and 1 pack of pens for a total cost of 21.60.
We can set up the tape diagram as follows:
1. Use one rectangular tile labeled "36.8 =" to represent the total cost of Keith's purchase.
2. Below it, draw another rectangular tile labeled "21.6 =" to represent the total cost of Reina's purchase.
3. For both diagrams, you can represent each notebook with a tile labeled "N" and each pack of pens with a tile labeled "P."
The resulting tape diagrams can be named like this:
- Keith's purchase: 4N + 3P = 36.80
- Reina's purchase: 4N + 1P = 21.60
### PART B: Cost of One Notebook and One Pack of Pens
To find the cost of one notebook and one pack of pens, we will set up the following equations based on the information provided:
1. From Keith's purchase:
\[
4N + 3P = 36.80 \quad \text{(1)}
\]
2. From Reina's purchase:
\[
4N + 1P = 21.60 \quad \text{(2)}
\]
Now we can solve these equations.
**Step 1: Subtract equation (2) from equation (1)**:
\[
(4N + 3P) - (4N + 1P) = 36.80 - 21.60
\]
This simplifies to:
\[
2P = 15.20
\]
Dividing both sides by 2 gives:
\[
P = 7.60
\]
**Step 2: Substitute P back into one of the original equations to find N. I will use equation (2) for that**:
\[
4N + 1(7.60) = 21.60
\]
This simplifies to:
\[
4N + 7.60 = 21.60
\]
Subtracting 7.60 from both sides gives:
\[
4N = 14.00
\]
Dividing both sides by 4 gives:
\[
N = 3.50
\]
### Final Answers
- One notebook: **3.50**
- One pack of pens: **7.60**