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≥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 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<2n

0.25p+4n≤100

Answer 1

To represent the constraints in this scenario as a system of inequalities, we need to consider the requirements given.

1. The number of pencils (p) needed is at least twice the number of notebooks (n):
\[
p \geq 2n
\]

2. The cost of the pencils and notebooks cannot exceed her budget of $100. The cost can be expressed as:
\[
0.25p + 4n \leq 100
\]

Based on the information provided, the correct representation of the constraints is:

\[
p \geq 2n
\]
\[
0.25p + 4n \leq 100
\]

Therefore, the appropriate response from the options is:
- **p ≥ 2n**
- **0.25p + 4n ≤ 100**

This matches the second option listed in your choices.