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This problem describes a scenario where the total cost of an order from an online candy store depends on the weight of the candy (in pounds) and a fixed shipping cost. The total cost is represented as:

\[
\text{Total Cost} = (\text{Cost per pound of candy} \times \text{Weight of candy}) + \text{Fixed shipping cost}
\]

The table provides the following dataThis problem describes a scenario where the total cost of an order from an online candy store depends on the weight of the candy (in pounds) and a fixed shipping cost. The total cost is represented as:

\[
\text{Total Cost} = (\text{Cost per pound of candy} \times \text{Weight of candy}) + \text{Fixed shipping cost}
\]

The table provides the following 

| Weight of Candy (in pounds) | Total Cost |
|-----------------------------|------------|
| 3                           | $13.50     |
| 7                           | $23.50     |
| 10                          | $31.00     |

Let's define the following:
- Let **$ p $** be the cost per pound of candy.
- Let **$ S $** be the fixed shipping cost.

We now have three equations based on the table:

1. For 3 pounds:  
\[
3p + S = 13.50
\]

2. For 7 pounds:  
\[
7p + S = 23.50
\]

3. For 10 pounds:  
\[
10p + S = 31.00
\]

### Step 1: Subtract the first equation from the second to eliminate $ S $.

\[
(7p + S) - (3p + S) = 23.50 - 13.50
\]

This simplifies to:

\[
4p = 10
\]

Thus, $ p = 2.50 $, which means the cost per pound of candy is $2.50.

### Step 2: Substitute $ p = 2.50 $ into one of the original equations (let's use the first equation) to find $ S $:

\[
3(2.50) + S = 13.50
\]

\[
7.50 + S = 13.50
\]

\[
S = 6.00
\]

So, the fixed shipping cost is $6.00.

### Step 3: Evaluate the answer choices:

- **A**: The cost per pound of candy is **$2.50** – This is **true**.
- **B**: The cost per pound of candy is **$10.00** – This is **false**.
- **C**: The fixed shipping cost is **$11.00** – This is **false**.
- **D**: The fixed shipping cost is **$13.50** – This is **false**.

### Correct Answer: **A**

Would you like further details or have any questions?

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Here are five related questions to expand your understanding:

1. How would the total cost change if the shipping cost increased by $2.00?
2. What if the weight of candy was 15 pounds, how would you calculate the total cost?
3. Can you set up a general formula for total cost based on the values of $ p $ and $ S $?
4. How can we interpret this situation graphically with weight as the $ x $-axis and total cost as the $ y $-axis?
5. How would the equation change if there was a different cost per pound for larger orders?

**Tip:** Always start by isolating one variable to simplify systems of equations.

An online candy store calculates the total cost of an order as a function of the weight, in pounds, of the candy plus a fixed shipping cost. The table shows the total cost of three candy orders of different weights. According to the table, which statement is true?

Explore how to determine the cost per pound of candy and fixed shipping costs using linear equations. This guide provides a step-by-step breakdown of solving systems of equations based on the total cost affected by the candy weight and shipping. Suitable for students in Grades 8-10.

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