Let $x$ be the price of a large candle, and $y$ be the price of a small candle. We can set up the following equations based on the information provided:

1. From the first customer: $3x + 4y = 64$

2. From the second customer, who paid $4 more: $x + 8y = 64 + 4 = 68$

Now, we can solve these two equations step by step.

Step 1: Solve the second equation for $x$

From the second equation: $x + 8y = 68$ $x = 68 - 8y$

Step 2: Substitute $x$ into the first equation

Now substitute $x$ into the first equation: $3(68 - 8y) + 4y = 64$ Distributing: $204 - 24y + 4y = 64$ Combine like terms: $204 - 20y = 64$

Step 3: Solve for $y$

Subtract 204 from both sides: $-20y = 64 - 204$ $-20y = -140$ Divide both sides by -20: $y = 7$

Step 4: Substitute $y$ back to find $x$

Now substitute $y = 7$ back into the equation for $x$: $x = 68 - 8(7)$ $x = 68 - 56$ $x = 12$

Thus, the price of each candle is:

• Large candle: $x = 12$
• Small candle: $y = 7$

The small candle cost $7.

If you have any questions or need further details, feel free to ask! Here are some follow-up questions you might consider:

1. What would be the total cost if a customer bought 2 large candles and 5 small candles?
2. How much would the first customer have saved if each candle was discounted by $2?
3. If a third customer bought 4 large candles, how much would they pay?
4. What is the price ratio of a large candle to a small candle?
5. If the price of small candles increased by 10%, what would be their new price?

Tip: When dealing with systems of equations, substitution is a powerful method to simplify the problem!