Work-rate from a given case, then scale to a new target: 5 boys take 7 hours to pack 35 toys. How many boys are required to pack 65 toys in 3 hours, assuming all work at the same constant rate?

Introduction / Context:
Here we infer the group productivity from a known case and then scale it to meet a different production target within a different time window. The method is a straightforward application of proportion based on (boys * hours) = toys / productivity per boy-hour.

Given Data / Assumptions:

• 5 boys * 7 hours produce 35 toys.
• Assume linear productivity and no setup overheads; all boys identical.
• Goal: 65 toys in 3 hours.

Concept / Approach:
First compute toys per boy-hour from the given case, then compute required boy-hours for 65 toys, and finally divide by 3 hours to get boys needed. Round up to the next whole number since a fraction of a boy is not possible in headcount terms.

Step-by-Step Solution:
From the given: (5 * 7) boy-hours produce 35 toys ⇒ 35 / 35 = 1 toy per boy-hour.Required boy-hours for 65 toys = 65 / 1 = 65 boy-hours.In 3 hours, boys needed = 65 / 3 ≈ 21.666…, i.e., 22 boys.

Verification / Alternative check:
If 22 boys work 3 hours, total boy-hours = 66, and toys at 1 toy per boy-hour = 66 ≥ 65. With 21 boys, only 63 toys result, which is insufficient.

Why Other Options Are Wrong:

• 26, 39, 45 greatly exceed the minimum required 22 and are not the least feasible integer headcount.

Common Pitfalls:

• Treating 21.666… as 21 instead of rounding up to ensure the target is met.

Final Answer:
None of these