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 less than 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

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

To represent the constraints of the scenario as a system of inequalities, we need to outline two key constraints based on the problem description:

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

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

Combining these two inequalities, we represent the constraints of the scenario as:
- \( p \geq 2n \)
- \( 0.25p + 4n \leq 100 \)

Therefore, the correct response is:
**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**