Output scaling with workers and days: Four mat-weavers weave 4 mats in 4 days at a constant rate. At this same rate, how many mats would 8 mat-weavers weave in 8 days?

Introduction / Context:
The production of mats is proportional to the product of the number of weavers and the number of days, provided each weaver works at the same constant efficiency. This is a straightforward scaling exercise using the unitary method across workers and time.

Given Data / Assumptions:

• 4 weavers produce 4 mats in 4 days
• Target scenario: 8 weavers, 8 days
• Efficiency per weaver is constant.

Concept / Approach:
Compute the per-weaver-per-day output from the initial scenario. Then scale up for more weavers and more days to get the total output under the new scenario.

Step-by-Step Solution:
Per-weaver-per-day rate = 4 mats / (4 weavers * 4 days) = 4 / 16 = 0.25 matTotal mats = 0.25 * 8 weavers * 8 days = 16 mats

Verification / Alternative check:
Proportionality shortcut: Doubling weavers and doubling days multiplies output by 4. From 4 mats → 16 mats. Same answer.

Why Other Options Are Wrong:
12 and 14 undercount; 18 and 20 overcount relative to the implied production rate of 0.25 mat per weaver per day.

Common Pitfalls:
Assuming “4 weavers produce 4 mats in 4 days” means 1 mat per weaver per day, which is incorrect. The correct interpretation is total output shared by all weavers over all days.

Final Answer:
16