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 $_______. 


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**4b.** 

The large candle cost $_______

Let's set up the problem with variables and equations:  
- Let **L** be the price of a large candle.  
- Let **S** be the price of a small candle.  

From the problem, we know the following:

1. **First customer**:  
   $ 3L + 4S = 64 $  (Total payment by the first customer)

2. **Second customer**:  
   $ 1L + 8S = 64 + 4 = 68 $ (Total payment by the second customer)

### Step 1: Solve one equation for L in terms of S  
From the second equation:  
\[
1L + 8S = 68 \quad \Rightarrow \quad L = 68 - 8S
\]

### Step 2: Substitute into the first equation  
Now substitute $ L = 68 - 8S $ into the first equation $ 3L + 4S = 64 $:

\[
3(68 - 8S) + 4S = 64
\]

### Step 3: Simplify the equation  
Distribute the 3:  
\[
204 - 24S + 4S = 64
\]

Combine like terms:  
\[
204 - 20S = 64
\]

Move 204 to the other side:  
\[
-20S = 64 - 204 = -140
\]

Solve for $ S $:  
\[
S = \frac{-140}{-20} = 7
\]

Thus, the price of a **small candle** is:
\[
S = 7
\]

### Step 4: Find the price of a large candle  
Now substitute $ S = 7 $ into the equation $ L = 68 - 8S $:

\[
L = 68 - 8(7) = 68 - 56 = 12
\]

Thus, the price of a **large candle** is:
\[
L = 12
\]

### Final Answers:
- **Small candle**: $7  
- **Large candle**: $12

Would you like to see these calculations visualized in another way or have any further questions?

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Here are 5 questions related to this problem:
1. What happens if the second customer paid $10 more instead of $4 more?
2. How would the solution change if the two equations were inconsistent (no solution)?
3. Can you set up a system of equations for three variables with three customers?
4. What if the large candle’s price increased by 20%—how would the equations change?
5. How would you solve the problem if only the total price of 7 mixed candles was given?

**Tip:** When solving systems of equations, substitution works well with smaller numbers, while elimination might be faster for larger systems.

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?

Discover how to solve a real-life system of equations involving large and small candle prices. Learn step-by-step how a customer paid $64 for 3 large and 4 small candles, and how the price of each candle was determined. Suitable for students in Grades 7-10.

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