Edith tutors after school for which she gets paid at a rate of $20 an hour. She has also accepted a job as a library assistant that pays $15 an hour. She will work both jobs, but she is able to work no more than a total of 11 hours week, due to school commitments. Edith wants to earn at least $185 a week working a combination of both jobs. Which inequality can be used to represent the solution?

Options

A. `20(11+x)+(185)/(x)gt15`
B. `20x+15(11-x)gt185`
C. `15(11-x)+(185)/(x)gt20`
D. `15x+20(11+x)gt185`

Answer

To solve the problem, we need to set up inequalities based on the information provided about Edith's work hours and earnings.

### Step-by-Step Solution:

1. **Define Variables:**
Let \( X \) be the number of hours Edith works as a tutor, and \( Y \) be the number of hours she works as a library assistant.

2. **Total Hours Constraint:**
According to the problem, Edith can work no more than 11 hours a week. This gives us the equation:
\[ X + Y \leq 11 \]

3. **Income from Each Job:**
- The income from tutoring is \( 20X \) (since she earns $20 per hour).
- The income from the library assistant job is \( 15Y \) (since she earns $15 per hour).

4. **Total Income Requirement:**
Edith wants to earn at least $185 a week. This gives us the inequality:
\[ 20X + 15Y \geq 185 \]

5. **Substituting for Y:**
From the total hours constraint, we can express \( Y \) in terms of \( X \):
\[ Y = 11 - X \]
Now we substitute this expression for \( Y \) into the income inequality:
\[ 20X + 15(11 - X) \geq 185 \]

6. **Simplifying the Inequality:**
Distributing the 15:
\[ 20X + 165 - 15X \geq 185 \]
Combine like terms:
\[ 5X + 165 \geq 185 \]

7. **Isolating X:**
Subtract 165 from both sides:
\[ 5X \geq 20 \]
Divide by 5:
\[ X \geq 4 \]

8. **Final Inequality:**
Now we have the inequalities:
- For hours: \( X + Y \leq 11 \)
- For income: \( 20X + 15Y \geq 185 \)

### Conclusion:
The inequality that represents the solution is:
\[ 20X + 15Y \geq 185 \quad \text{and} \quad X + Y \leq 11 \]