Question

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)
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**