Allision is planting a garden with at least 15 trees. There will be a conbination of apple trees, which cost `$120` each, and pear trees, which cost `$145` each. Allision's budget for purchasing the trees is on more than `$2,050.` She must plane at least 5 people trees and at least 3 pear trees. Which of the following systems of inequaliteies represents the situation described if x is the number of apple trees and y is the number of pear trees ?

Options

A. `120x + 145 y ge 2,050`
`x +yle 15`
`x ge5`
`y ge 3`
B. `120x+145y ge 2,050`
`x +y ge 15`
`x le 5`
`y le3`
C. `120x +145 le 2,050`
`x +y ge 15`
`x le 5`
`y le 3`
D. `120x + 145y le 2,050`
`x +y ge 15`
`x ge 5`
`y ge 3`

Explanation

To represent the situation described in the problem with a system of inequalities, we need to analyze the conditions given for the number of apple trees (x) and pear trees (y).

### Step-by-Step Solution:

1. **Minimum Number of Apple Trees**:
- Allision must plant at least 5 apple trees.
- This can be represented as:
\[ x \geq 5 \]

**Hint**: Remember that "at least" means the number must be greater than or equal to the specified number.

2. **Minimum Number of Pear Trees**:
- Allision must plant at least 3 pear trees.
- This can be represented as:
\[ y \geq 3 \]

**Hint**: Similar to the first step, "at least" indicates that the number must be greater than or equal to the specified number.

3. **Total Number of Trees**:
- The total number of trees (apple trees + pear trees) must be at least 15.
- This can be represented as:
\[ x + y \geq 15 \]

**Hint**: When combining quantities, ensure you account for the total requirement as specified.

4. **Budget Constraint**:
- The cost of apple trees is $120 each, and the cost of pear trees is $145 each. The total cost must not exceed $2,050.
- This can be represented as:
\[ 120x + 145y \leq 2050 \]

**Hint**: When dealing with costs, multiply the number of trees by their respective costs and ensure the total is within the budget limit.

### Final System of Inequalities:
Combining all the inequalities derived from the conditions, we have the following system of inequalities:

\[ \begin{align*} 1. & \quad x \geq 5 \\ 2. & \quad y \geq 3 \\ 3. & \quad x + y \geq 15 \\ 4. & \quad 120x + 145y \leq 2050 \\ \end{align*} \]