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 large candle is the same, and the price of each small candle is the same.

How much did each candle cost?

The small candle cost $_______. 

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!

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 large candle is the same, and the price of each small candle is the same. How much did each candle cost?

Explore how to find the price of large and small candles using systems of equations. This problem involves two customers and their respective purchases, leading to a solution for the cost of each candle. Ideal for students in Grades 7-9.

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