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!