Final answer:
To satisfy the time constraint of completing his exam in 2 hours, Ben must adhere to the inequality 30p + 10q ≤ 120, where p is the number of poems and q is the number of paragraphs. Additionally, he must write at least 10 items combined, so the inequality p + q ≥ 10 also applies. Balancing these inequalities will allow Ben to complete his creative writing exam within the given constraints.
Step-by-step explanation:
The question involves setting up inequalities to represent both the time constraint and the minimum item requirement for Ben's creative writing exam. To write an inequality based on the time constraint, we must consider that Ben has 2 hours (or 120 minutes) to complete the exam. Given that each poem takes 30 minutes to write and each paragraph takes 10 minutes, if p represents the number of poems and q represents the number of paragraphs, the inequality representing the time constraint would be 30p + 10q ≤ 120.
The second inequality based on the number of items needed must consider that Ben needs to complete at least 10 poems or paragraphs combined. Therefore, the inequality representing this requirement is p + q ≥ 10.
To provide a solution that satisfies both constraints, let's imagine Ben chooses to write 3 poems; this would use up 90 minutes. He would then have 30 minutes left to write paragraphs, allowing for 3 additional paragraphs. Ben has written more than the minimum requirement (3 poems + 3 paragraphs = 6 items) but has not exceeded the time limit. This is just one possible solution, and other combinations of poems and paragraphs could also satisfy both inequalities.