Each student in the choir must earn $2500 to attend a performance in Ireland this summer. To earn the funds they are selling candy bars and t-shirts. For each candy bar sold, the singer earns $1 credit, and for each t-shirt the singer earn $5.75. Which equation represents the number of candy bars (X) and t-shirts (y) that must be sold by each singer to ensure that he/she can attend the performance ?

Options

A. `(x+1)+(y+5.75)ge2500`
B. `5.75x+yge2500`
C. `x+5.75yge2500`
D. `6.75xyge2500`

Answer

To solve the problem, we need to formulate an equation based on the information provided about the earnings from selling candy bars and t-shirts.

### Step-by-Step Solution:

1. **Identify Variables**:
- Let \( X \) represent the number of candy bars sold.
- Let \( Y \) represent the number of t-shirts sold.

2. **Determine Earnings from Candy Bars**:
- Each candy bar sold earns the student $1.
- Therefore, the total earnings from selling \( X \) candy bars is:
\[ \text{Earnings from candy bars} = 1 \times X = X \text{ dollars} \]

3. **Determine Earnings from T-Shirts**:
- Each t-shirt sold earns the student $5.75.
- Therefore, the total earnings from selling \( Y \) t-shirts is:
\[ \text{Earnings from t-shirts} = 5.75 \times Y = 5.75Y \text{ dollars} \]

4. **Set Up the Total Earnings Equation**:
- The total earnings from both candy bars and t-shirts must be at least $2500 for the student to attend the performance.
- This gives us the inequality:
\[ X + 5.75Y \geq 2500 \]

5. **Final Equation**:
- The equation that represents the number of candy bars \( X \) and t-shirts \( Y \) that must be sold is:
\[ X + 5.75Y \geq 2500 \]