When hired at a new job selling jewelry, you are given two pay options:

Option A: Base salary of $15,000 a year, with a commission of 10% of your sales

Option B: Base salary of $25,000 a year, with a commission of 3% of your sales

In order for option A to produce a larger income, you would need sell at least $
   of jewelry each year.

Let's calculate the amount of jewelry that needs to be sold each year for Option A to produce a larger income than Option B.

### Let:
- $ x $ represent the amount of jewelry sold (in dollars).

### Income from Option A:
- Base salary: $15,000
- Commission: 10% of sales → $ 0.10x $
- Total income: $ 15,000 + 0.10x $

### Income from Option B:
- Base salary: $25,000
- Commission: 3% of sales → $ 0.03x $
- Total income: $ 25,000 + 0.03x $

### Set the inequality for Option A to produce a larger income than Option B:

\[
15,000 + 0.10x > 25,000 + 0.03x
\]

### Solve the inequality:

1. Subtract $ 15,000 $ from both sides:
   \[
   0.10x > 10,000 + 0.03x
   \]

2. Subtract $ 0.03x $ from both sides:
   \[
   0.07x > 10,000
   \]

3. Divide by 0.07:
   \[
   x > \frac{10,000}{0.07}
   \]

   \[
   x > 142,857.14
   \]

So, in order for Option A to produce a larger income than Option B, you would need to sell at least **$142,857.14** of jewelry each year.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the total income for Option A if you sell $200,000 worth of jewelry?
2. What is the total income for Option B if you sell $150,000 worth of jewelry?
3. How much would you need to sell to make the same income from both options?
4. What is the commission difference between the two options at $100,000 in sales?
5. How would the required sales change if the commission rate in Option B increased to 5%?

**Tip:** When choosing between pay structures with commissions, calculate the breakeven point to determine which option benefits you based on expected sales.

When hired at a new job selling jewelry, you are given two pay options: Option A: Base salary of $15,000 a year, with a commission of 10% of your sales. Option B: Base salary of $25,000 a year, with a commission of 3% of your sales. In order for option A to produce a larger income, you would need to sell at least $_____ of jewelry each year.

Learn how to compare two pay options using a linear inequality. We calculate how much jewelry you need to sell each year for Option A to produce a larger income than Option B. This problem covers algebraic concepts and inequality solving, suitable for high school students in Grades 9-12.

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