Amy needs to purchase pencils and notebooks for her students. The number of pencils needed is at least twice as many as the number of notebooks. The pencils cost $0.25 each and the notebooks cost $4. Amy’s budget for these supplies allows for a maximum cost of $100. How do you represent the constraints of this scenario as a system of inequalities, where p is the number of pencils and n is the number of notebooks Amy will buy?(1 point

To represent the constraints of Amy's scenario as a system of inequalities, we need to consider the two given conditions: the relationship between the number of pencils and notebooks, and the budget constraint.

1. The first condition states that the number of pencils (p) needed is at least twice the number of notebooks (n). This can be expressed as:

   \[ p \geq 2n \]

2. The second condition relates to the budget. The cost of pencils is $0.25 each and the cost of notebooks is $4 each. Therefore, the total cost can be expressed as:

   \[ 0.25p + 4n \leq 100 \]

Combining these two inequalities, we get the following system of inequalities to represent the constraints:

\[ \begin{align*}

1. & \quad p \geq 2n \
2. & \quad 0.25p + 4n \leq 100 \end{align*} \]

Additionally, since quantities of pencils and notebooks can't be negative, we can include non-negativity constraints:

\[ p \geq 0 \quad \text{and} \quad n \geq 0 \]

Thus, the complete system of inequalities is:

\[ \begin{align*}

1. & \quad p \geq 2n \
2. & \quad 0.25p + 4n \leq 100 \
3. & \quad p \geq 0 \
4. & \quad n \geq 0 \end{align*} \]