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The problem states that Luis wants to earn at least $1,200 this week. He is paid a weekly salary of $400 plus a 5.2% commission on his total weekly sales. We need to find the minimum amount Luis needs to sell to meet his goal.

### Let's define the variables:
- Let $ x $ be the total sales Luis needs to make.
- His total earnings will be the sum of his salary and commission:
  
  \[
  \text{Earnings} = 400 + 0.052 \times x
  \]

### Luis's goal is to earn at least $1,200:
  
  \[
  400 + 0.052 \times x = 1,200
  \]

### Solving for $ x $:

1. Subtract 400 from both sides:
   \[
   0.052 \times x = 1,200 - 400
   \]
   \[
   0.052 \times x = 800
   \]

2. Divide both sides by 0.052:
   \[
   x = \frac{800}{0.052} \approx 15,384.62
   \]

So, Luis needs to make **at least $15,385** in sales to meet his goal (rounded to the nearest dollar).

Would you like more details or further clarification? 

### Related questions:
1. What if Luis had a higher commission rate, say 7%? How would his required sales change?
2. How much would Luis need to sell if his salary were $500 instead of $400?
3. How much commission would Luis earn if he sold $10,000 worth of goods?
4. If Luis earns an additional $50 bonus for every $5,000 in sales, how much would he need to sell to make $1,200?
5. What would Luis's total earnings be if he sold $20,000 worth of goods?

### Tip: When dealing with commission problems, always separate fixed income (like salary) from variable income (like commission) to simplify calculations.

Luis wants to earn at least $1,200 this week. He is paid a weekly salary of $400 plus a 5.2% commission on his total weekly sales. What is the minimum amount he needs to sell in order to reach his goal?

Learn how to calculate the minimum sales Luis needs to reach his weekly earnings goal of $1,200. He earns a salary of $400 plus a 5.2% commission on sales. This problem covers algebra, percentages, and solving linear equations, perfect for students in Grades 6-8.

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