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Let's solve these problems step-by-step.

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### Problem 65:
**Given:**
- Base salary = $2,150  
- Commission = 8% of sales over $7,000  
- Desired total earnings = $3,170  

**Solution:**  
Let $ x $ represent the total sales amount for the month.

1. **Identify commission on sales over $7,000**:  
   If total sales are $ x $, the sales eligible for commission are $ x - 7,000 $ (only if $ x > 7,000 $).

2. **Write the total earnings equation:**  
   Base salary + Commission = Total earnings  
   \[
   2150 + 0.08(x - 7000) = 3170
   \]

3. **Solve for $ x $:**  
   - Subtract 2150 from both sides:  
     \[
     0.08(x - 7000) = 3170 - 2150
     \]
     \[
     0.08(x - 7000) = 1020
     \]
   - Divide both sides by 0.08:  
     \[
     x - 7000 = \frac{1020}{0.08}
     \]
     \[
     x - 7000 = 12,750
     \]
   - Add 7,000 to both sides:  
     \[
     x = 19,750
     \]

**Answer for Problem 65:**  
The employee must sell **$19,750** in 1 month to earn a total of $3,170.

---

### Problem 66 (A):
**Given:**
- Base salary = $1,175  
- Commission = 5% on all sales  
- Desired total earnings = $3,170  

**Solution:**  
Let $ x $ represent the total sales amount.

1. **Write the total earnings equation:**  
   Base salary + Commission = Total earnings  
   \[
   1175 + 0.05x = 3170
   \]

2. **Solve for $ x $:**  
   - Subtract 1175 from both sides:  
     \[
     0.05x = 3170 - 1175
     \]
     \[
     0.05x = 1995
     \]
   - Divide both sides by 0.05:  
     \[
     x = \frac{1995}{0.05}
     \]
     \[
     x = 39,900
     \]

**Answer for Problem 66(A):**  
The second employee must sell **$39,900** to earn $3,170.

---

### Problem 66 (B):
**Determine the sales level where both employees receive the same income.**

**Solution:**  
Let $ x $ represent the total sales for both employees.

1. **Write the income equations:**
   - Employee 1: $ 2150 + 0.08(x - 7000) $ for $ x > 7,000 $  
   - Employee 2: $ 1175 + 0.05x $

2. **Set the two equations equal:**  
   \[
   2150 + 0.08(x - 7000) = 1175 + 0.05x
   \]

3. **Simplify and solve for $ x $:**  
   - Expand the left-hand side:  
     \[
     2150 + 0.08x - 560 = 1175 + 0.05x
     \]
     Combine constants:  
     \[
     1590 + 0.08x = 1175 + 0.05x
     \]
   - Subtract 0.05x from both sides:  
     \[
     1590 + 0.03x = 1175
     \]
   - Subtract 1590 from both sides:  
     \[
     0.03x = 1175 - 1590
     \]
     \[
     0.03x = -415
     \]

Since this doesn't make sense, and we're left

65. One employee of a computer store is paid a base salary of $2,150 a month plus an 8% commission on all sales over $7,000 during the month. How much must the employee sell in 1 month to earn a total of $3,170 for the month?
66. A second employee of the computer store in Problem 65 is paid a base salary of $1,175 a month plus a 5% commission on all sales during the month.
(A) How much must this employee sell in 1 month to earn a total of $3,170 for the month?
(B) Determine the sales level where both employees receive the same monthly income. If employees can select either of these payment methods, how would you advise an employee to make this selection?

Learn how to calculate the sales needed for two employees to earn the same monthly income under different commission structures. The problem explores linear equations and commission-based salary calculations, ideal for students in Grades 9-12.

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