If 3 pencils and 2 erasers cost $17 and 1 pencil and 4 erasers cost $13, how much do 5 pencils and 5 erasers cost? Give simple step by step explanation for grade 3 students.

Let's break it down step by step:

### Step 1: Understand the problem.
- We know the prices of two groups of pencils and erasers:
  - **3 pencils + 2 erasers = $17**
  - **1 pencil + 4 erasers = $13**
- We need to find how much **5 pencils and 5 erasers** cost.

### Step 2: Use letters for unknown prices.
- Let **P** be the price of one pencil.
- Let **E** be the price of one eraser.

### Step 3: Write equations.
1. From the first group:  
   **3P + 2E = 17**  (Equation 1)
2. From the second group:  
   **P + 4E = 13**  (Equation 2)

### Step 4: Solve the equations.

#### Step 4.1: Rearrange Equation 2.
We want to isolate **P**.  
From **P + 4E = 13**, we get:  
**P = 13 - 4E**

#### Step 4.2: Substitute in Equation 1.
Now, replace **P** in **3P + 2E = 17** using **P = 13 - 4E**:  
**3(13 - 4E) + 2E = 17**

Now solve it step by step:  
**39 - 12E + 2E = 17**  
**39 - 10E = 17**  
Subtract 39 from both sides:  
**-10E = -22**  
Divide both sides by -10:  
**E = 2.2**

#### Step 4.3: Find the price of a pencil.
Now that we know **E = 2.2**, substitute this value into **P = 13 - 4E**:  
**P = 13 - 4(2.2)**  
**P = 13 - 8.8**  
**P = 4.2**

### Step 5: Find the total cost of 5 pencils and 5 erasers.
Now we know:  
- One pencil (P) costs **4.2 dollars**.  
- One eraser (E) costs **2.2 dollars**.

So:  
**5 pencils = 5 × 4.2 = 21 dollars**  
**5 erasers = 5 × 2.2 = 11 dollars**  

Total cost = **21 + 11 = 32 dollars**

### Final Answer:
The total cost of **5 pencils and 5 erasers** is **$32**.

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Do you want more details or have any questions?  

Here are 5 related questions:
1. What if 2 pencils and 3 erasers cost $15? Can you find their individual prices?
2. How do we solve equations with two variables faster?
3. What would happen if one eraser cost 3 dollars? How would the answer change?
4. How can we check if our answer is correct?
5. Can we solve this using a graph?

**Tip:** When solving word problems, always define your variables clearly to avoid confusion.

Learn to calculate the total cost of 5 pencils and 5 erasers when given the combined costs of pencils and erasers. This step-by-step guide explains the substitution method and basic algebra concepts in a way suitable for Grade 3 students.

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