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)

Question

Responses

p≥2n

0.25p+4n≤100

p greater-than-or-equal-to 2 n 0.25 p plus 4 n less-than-or-equal-to 100

p≥2n

0.25p+4n≥100

p greater-than-or-equal-to 2 n 0.25 p plus 4 n greater-than-or-equal-to 100

p≥n+2

0.25p+4n≤100

p greater-than-or-equal-to n plus 2 0.25 p plus 4 n less-than-or-equal-to 100

p<2n

0.25p+4n≤100

p less than 2 n 0.25 p plus 4 n less-than-or-equal-to 100
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Answer 1

To represent the constraints of Amy's scenario as a system of inequalities, we need to summarize the information provided about the pencils and notebooks.

1. The number of pencils (p) needed is at least twice the number of notebooks (n), which can be expressed as: \[ p \geq 2n \]

2. The total cost must not exceed her budget of $100. Since the pencils cost $0.25 each and the notebooks cost $4, this can be expressed as: \[ 0.25p + 4n \leq 100 \]

Combining these two inequalities, we get the system: \[ \begin{align*} p & \geq 2n \ 0.25p + 4n & \leq 100 \end{align*} \]

Thus, the correct representation of the constraints is:

• \( p \geq 2n \)
• \( 0.25p + 4n \leq 100 \)

This matches the first response option:

• p≥2n
• 0.25p+4n≤100