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≥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.