If 8 pens and 4 rulers cost $116 and 2 pens and 6 rulers cost$54. Find the cost of 30 pens and 30 rulers. Give simple step by step explanation for Grade 3 students.

Let’s solve this together, step by step.

### Step 1: Write down what we know.
We have two pieces of information:
1. **8 pens + 4 rulers = $116**
2. **2 pens + 6 rulers = $54**

Let’s say:
- Each pen costs **P** dollars.
- Each ruler costs **R** dollars.

So, we can write the information as two math sentences (equations):
- **8P + 4R = 116**
- **2P + 6R = 54**

### Step 2: Make the math simpler.
Let’s make these equations easier to work with.

1. **8P + 4R = 116** — We can divide everything here by 4:
   - This becomes **2P + R = 29**

2. So now we have two simpler equations:
   - **2P + R = 29**
   - **2P + 6R = 54**

### Step 3: Subtract to find R (cost of a ruler).
Now we can subtract the first equation from the second one to get **R**.

1. **(2P + 6R) - (2P + R) = 54 - 29**
2. This simplifies to **5R = 25**
3. Divide by 5: **R = 5**

So, **each ruler costs $5**.

### Step 4: Find P (cost of a pen).
Now we can use **R = 5** in the first equation to find **P**.

1. **2P + R = 29**
2. Substitute **R = 5**:
   - **2P + 5 = 29**
3. Subtract 5 from both sides: **2P = 24**
4. Divide by 2: **P = 12**

So, **each pen costs $12**.

### Step 5: Find the cost of 30 pens and 30 rulers.
Now, we know:
- Each pen costs $12.
- Each ruler costs $5.

To find the cost of 30 pens and 30 rulers:
1. **Cost of 30 pens = 30 x 12 = $360**
2. **Cost of 30 rulers = 30 x 5 = $150**

Add them together:
- **Total cost = $360 + $150 = $510**

### Final Answer:
The cost of 30 pens and 30 rulers is **$510**.

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Would you like more details or have any questions?

### Practice Questions
1. If 10 pens and 5 rulers cost $X, how much is X?
2. How much would 5 pens and 2 rulers cost?
3. What if the cost of 3 pens and 7 rulers was needed?
4. Can you find the cost of 15 pens and 20 rulers?
5. How much would it be to buy 50 pens only?

**Tip:** When you have two equations, try simplifying them to make solving easier!

If 8 pens and 4 rulers cost $116 and 2 pens and 6 rulers cost $54, find the cost of 30 pens and 30 rulers. Give a simple step-by-step explanation for Grade 3 students.

Learn how to find the cost of 30 pens and 30 rulers using basic algebra with a step-by-step solution suitable for Grade 3 students. This problem includes solving a system of equations to find individual item costs and calculate total expenses.

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