Question

devin is collecting signatures for a petition to open a new park in her town. she needs to collect at least 1,000 signatures before she can schedule a meeting with the mayor. she already has 380 signatures. if each petition page holds 80 signatures, which inequality best shows how many more pages \\(p\\) devin needs?

• \\(8 < p\\)
• \\(8 \le p\\)
• \\(9 < p\\)
• \\(7 \le p\\)

Explanation:

Identify the target goal and given values

Using the Writing Linear Inequalities and Real-world Inequality Constraints knowledge points

• Total signatures needed: at least \(1,000\)
• Signatures already collected: \(380\)
• Signatures per page: \(80\)
• Variable \(p\): number of additional pages needed

Set up the inequality

Using the Writing Linear Inequalities knowledge point

$$ 380 + 80p \ge 1000 $$

Solve for the number of pages

Using the Real-world Inequality Constraints knowledge point

$$
LATEXBLOCK0
$$

Apply discrete constraints to find the correct option

Using the Discrete Quantities knowledge point

• Since pages must be whole numbers, \(p\) must be an integer.
• The smallest integer satisfying \(p \ge 7.75\) is \(8\).
• Therefore, Devin needs at least \(8\) more pages, which is represented by \(8 \le p\).

Answer:

• (A) \(8 < p\)
• (B) \(8 \le p\) (Correct answer)
• (C) \(9 < p\)
• (D) \(7 \le p\)