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?
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

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 of Amy's scenario with a system of inequalities, we need to consider the following:

1. The number of pencils (p) must be at least twice the number of notebooks (n).
2. The total cost of the pencils and notebooks must not exceed her budget of $100.

Given these conditions, we can express them as follows:

1. The first condition translates to:
\[
p \geq 2n
\]

2. The second condition relates to the costs. Pencils cost $0.25 each and notebooks cost $4 each, so the cost constraint is:
\[
0.25p + 4n \leq 100
\]

Putting these together, the system of inequalities that represents the constraints is:
\[
\begin{align*}
p & \geq 2n \\
0.25p + 4n & \leq 100
\end{align*}
\]

Thus, the correct answer is:
**p ≥ 2n**
**0.25p + 4n ≤ 100**