Work and wages proportionality: If a team of 6 persons working 8 hours per day earns $8400 in one week (same number of working days), then assuming earnings are directly proportional to total person-hours, how much will be earned in a week when 9 persons work 6 hours per day under the same pay rate?

Introduction / Context:
This question checks proportional reasoning in work-and-wages. When the pay rate per person-hour is constant and the number of working days in the week is the same for both cases, total weekly earnings are proportional to the product of the number of persons and the daily hours they work.

Given Data / Assumptions:

• Case 1: 6 persons, 8 hours/day, weekly earning = $8400.
• Case 2: 9 persons, 6 hours/day, weekly earning = unknown.
• Number of working days in the week is the same in both situations.
• Pay rate per person-hour is unchanged.

Concept / Approach:
If rate per person-hour is constant and days are equal, earnings scale with person-hours/day. So Earnings_2 / Earnings_1 = (Persons_2 * Hours_2) / (Persons_1 * Hours_1). Compute this ratio and multiply by the first week’s earnings to get the second week’s amount.

Step-by-Step Solution:

Verification / Alternative check:
Any common factor in working days cancels from both cases: only persons * hours/day matters. The factor 1.125 converts $8400 to $9450 exactly.

Why Other Options Are Wrong:
$16800 and $16200 imply much higher person-hours than given. $8400 assumes no change. $9000 is an arbitrary nearby figure not matching the precise ratio.

Common Pitfalls:
Forgetting that both scenarios cover equal numbers of days; using hours rather than person-hours; or assuming linearity with only persons or only hours.

Final Answer:
$9450