The ninth grade class class at a local high school needs to purchase a park permit for $250.00 for their upcoming class picnic. Each ninth grader attending pays $0.75. Each guest pays $1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?

Options

A. `0.75x-(1.25)(200)ge250.00`
B. `0.75x+(1.25)(200)ge250.00`
C. `(0.75)(200)-1.25xge250.00`
D. `(0.75)(200)+1.25xge250.00`

Answer

To solve the problem, we need to determine the total amount of money collected from the ninth graders and guests, and set up an inequality to ensure that this total is at least $250.

### Step-by-Step Solution:

1. **Identify the contributions from ninth graders:**
Each ninth grader pays $0.75. If there are 200 ninth graders attending, the total contribution from them can be calculated as:
\[ \text{Total from ninth graders} = 200 \times 0.75 \]

2. **Calculate the total contribution from ninth graders:**
\[ 200 \times 0.75 = 150 \]
So, the ninth graders will contribute $150.

3. **Identify the contributions from guests:**
Let \( x \) be the number of guests attending. Each guest pays $1.25, so the total contribution from the guests can be expressed as:
\[ \text{Total from guests} = 1.25x \]

4. **Set up the inequality:**
The total amount collected from both ninth graders and guests must be at least $250 to cover the park permit. Therefore, we can set up the inequality:
\[ 150 + 1.25x \geq 250 \]

5. **Rearranging the inequality:**
To isolate \( x \), we can subtract 150 from both sides:
\[ 1.25x \geq 250 - 150 \]
\[ 1.25x \geq 100 \]

6. **Final inequality:**
The inequality that can be used to determine the number of guests \( x \) needed to cover the cost of the permit is:
\[ 1.25x \geq 100 \]

### Conclusion:
The correct inequality that represents the situation is:
\[ 0.75 \times 200 + 1.25x \geq 250 \]
This corresponds to option D from the original question.