Robert sells 5 bags of pecans for $38.25.

If the cost of the pecans varies directly with the number of bags sold, which of the following does NOT reflect the same relationship?

Select TWO correct answers.
A.12 bags for $91.80
B.9 bags for $68.85
C.2 bags for $15.30
D.3 bags for $22.80
E.14 bags for $107.80

To solve this problem, we need to determine the cost per bag of pecans and use it to check which of the options do not follow the same direct variation.

### Step 1: Find the cost per bag.
Robert sells 5 bags of pecans for $38.25. The cost per bag is:

\[
\text{Cost per bag} = \frac{38.25}{5} = 7.65 \, \text{dollars per bag}
\]

### Step 2: Check each option to see if the price corresponds to $7.65 per bag.
- **Option A**: 12 bags for $91.80  
  \[
  \frac{91.80}{12} = 7.65
  \]
  This option reflects the same relationship.

- **Option B**: 9 bags for $68.85  
  \[
  \frac{68.85}{9} = 7.65
  \]
  This option reflects the same relationship.

- **Option C**: 2 bags for $15.30  
  \[
  \frac{15.30}{2} = 7.65
  \]
  This option reflects the same relationship.

- **Option D**: 3 bags for $22.80  
  \[
  \frac{22.80}{3} = 7.60
  \]
  This option **does not** reflect the same relationship, since $7.60 ≠ 7.65.

- **Option E**: 14 bags for $107.80  
  \[
  \frac{107.80}{14} = 7.70
  \]
  This option **does not** reflect the same relationship, since $7.70 ≠ 7.65.

### Conclusion:
The two options that do **not** reflect the same direct variation relationship are:
- **Option D (3 bags for $22.80)**
- **Option E (14 bags for $107.80)**

Would you like more details on this problem? Here are five related questions you might find helpful:

1. What is direct variation, and how does it apply in this context?
2. How would you solve this problem if the price per bag was unknown?
3. How does indirect variation differ from direct variation in such problems?
4. How can we graph the relationship between the number of bags and their cost?
5. How do you handle problems with multiple variables or proportional relationships?

**Tip**: Always double-check unit prices when comparing proportional relationships!

Robert sells 5 bags of pecans for $38.25. If the cost of the pecans varies directly with the number of bags sold, which of the following does NOT reflect the same relationship? Select TWO correct answers. A. 12 bags for $91.80 B. 9 bags for $68.85 C. 2 bags for $15.30 D. 3 bags for $22.80 E. 14 bags for $107.80

Learn how to solve a direct variation problem where Robert sells pecans, and the cost varies with the number of bags sold. This problem uses proportional reasoning to check which scenarios do not match the unit price of $7.65 per bag. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation