a laptop costs $1386 more than a printer. 4 laptops and 3 printers cost a total of $6,937. how much do a laptop and a printer cost altogether? can you show this in a bar model.

We can approach this problem step by step, using algebra to find the cost of the laptop and printer. We'll then break it down visually using a bar model.

### Step 1: Set up equations
Let:
- $ P $ be the cost of the printer.
- $ L $ be the cost of the laptop.

From the problem, we know:
1. A laptop costs $1386 more than a printer, so:
   \[
   L = P + 1386
   \]
2. The total cost of 4 laptops and 3 printers is $6,937, so:
   \[
   4L + 3P = 6937
   \]

### Step 2: Substitute $ L $ into the second equation
Substitute $ L = P + 1386 $ into the second equation:
\[
4(P + 1386) + 3P = 6937
\]
Now expand the equation:
\[
4P + 5544 + 3P = 6937
\]
Simplify:
\[
7P + 5544 = 6937
\]
Subtract 5544 from both sides:
\[
7P = 1393
\]
Solve for $ P $:
\[
P = \frac{1393}{7} = 199
\]

So, the printer costs **$199**.

### Step 3: Find the cost of the laptop
Now that we know the printer costs $199, substitute $ P = 199 $ into $ L = P + 1386 $:
\[
L = 199 + 1386 = 1585
\]
So, the laptop costs **$1585**.

### Step 4: Find the total cost of a laptop and a printer
The total cost of a laptop and a printer is:
\[
1585 + 199 = 1784
\]
Thus, the total cost of a laptop and a printer is **$1784**.

---

### Bar Model Representation

1. The **printer** cost can be represented by a single bar labeled $199.
2. The **laptop** is represented by two bars: 
   - One bar of the same length as the printer (to show the base cost of $199).
   - An additional bar of length corresponding to $1386, which shows how much more the laptop costs compared to the printer.

Let me know if you would like an image of the bar model.

---

Would you like further clarification or more details?

Here are 5 related questions:
1. If 3 laptops and 2 printers cost $X, how would you solve for $ X $?
2. What if the laptop was $2000 more than the printer? How would the equations change?
3. How would the total change if you bought 5 laptops and 2 printers instead?
4. What is the cost difference between 6 printers and 4 laptops?
5. How can you verify the solution is correct?

**Tip:** In word problems, breaking down complex statements into simple equations can help organize your approach.

A laptop costs $1386 more than a printer. 4 laptops and 3 printers cost a total of $6,937. How much do a laptop and a printer cost altogether? Can you show this in a bar model?

In this problem, we determine the cost of a laptop and a printer using linear equations. A laptop costs $1386 more than a printer, and the total cost of 4 laptops and 3 printers is $6937. Step-by-step solution and bar model representation included. Ideal for students in Grades 6-8.

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