Guys is paid $185 per week plus 3% of his total sales in dollar, and Jim is paid $275 per week plus 2.5% of his total sales in dollars. If d represents the dollars amount of sales for each person, which inequality represents the amount of sales for which Guy is paid more than Jim?

Options

A. `dgt18,000`
B. `dlt18,000`
C. `dgt12,500`
D. `dlt12,500`

Answer

To solve the problem, we need to set up the payment equations for both Guy and Jim based on their sales and then create an inequality to determine when Guy earns more than Jim.

1. **Guy's Earnings**:
- Guy is paid a fixed amount of $185 per week.
- He also earns 3% of his total sales, which can be expressed as \(0.03D\) (since 3% is the same as \(3/100\)).
- Therefore, Guy's total earnings can be represented as:
\[ \text{Guy's Earnings} = 185 + 0.03D \]

2. **Jim's Earnings**:
- Jim is paid a fixed amount of $275 per week.
- He earns 2.5% of his total sales, which can be expressed as \(0.025D\) (since 2.5% is the same as \(2.5/100\)).
- Therefore, Jim's total earnings can be represented as:
\[ \text{Jim's Earnings} = 275 + 0.025D \]

3. **Setting Up the Inequality**:
- We want to find out when Guy's earnings are greater than Jim's earnings. This can be expressed as:
\[ 185 + 0.03D > 275 + 0.025D \]

4. **Solving the Inequality**:
- First, we will subtract \(0.025D\) from both sides:
\[ 185 + 0.03D - 0.025D > 275 \]
- This simplifies to:
\[ 185 + 0.005D > 275 \]
- Next, we subtract 185 from both sides:
\[ 0.005D > 275 - 185 \]
- Simplifying the right side gives:
\[ 0.005D > 90 \]
- Finally, we divide both sides by 0.005 to isolate \(D\):
\[ D > \frac{90}{0.005} \]
- Calculating the division gives:
\[ D > 18000 \]

Thus, the inequality that represents the amount of sales for which Guy is paid more than Jim is:
\[ D > 18000 \]