https://file.aiquickdraw.com/mathbot/file/1729694822844vk0gkpnk.jpg

To solve this problem, we need to formulate a system of equations based on the information provided.

The key points are:
- A customer paid $64 for 3 large candles and 4 small candles.
- A second customer paid $4 more than the first customer (so $64 + $4 = $68) for 1 large candle and 8 small candles.
- We are asked to find the system of equations that represents this situation, where:
  - $ x $ is the price of a large candle.
  - $ y $ is the price of a small candle.

### Step 1: Create Equations
From the first piece of information:
- 3 large candles + 4 small candles = $64.
This gives us the equation:
\[
3x + 4y = 64
\]

From the second piece of information:
- 1 large candle + 8 small candles = $68.
This gives us the equation:
\[
x + 8y = 68
\]

### Step 2: Compare with Given Options
Now, we check which option matches the equations we've formed.

Looking at the answer choices:
1. $ 4y = 3x + 64 $ and $ 8y = x + 68 $ – This doesn't match.
2. $ 4y = 3x + 64 $ and $ 8y = x + 60 $ – This doesn't match.
3. $ 3x + 4y = 64 $ and $ x + 8y = 68 $ – This matches our equations.
4. $ 3x + 4y = 64 $ and $ x + 8y = 60 $ – The second equation is incorrect.

### Conclusion:
The correct system of equations is:
\[
\boxed{3x + 4y = 64 \quad \text{and} \quad x + 8y = 68}
\]

Would you like more details on solving these equations, or do you have any questions?

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Here are 5 related questions:
1. How do you solve a system of linear equations by substitution?
2. What is the graphical interpretation of solving two linear equations?
3. Can you explain how to set up equations for a word problem?
4. What happens if the system of equations has no solution?
5. How can systems of equations be applied in real-life scenarios?

**Tip:** When dealing with word problems, clearly define your variables and write down equations step-by-step to avoid confusion.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

Learn how to solve a word problem using a system of linear equations. This example focuses on determining the price of large and small candles using algebraic methods. Suitable for students in Grades 8-10.

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