Two boys and one girl can together complete a piece of work in 5 days, while one boy and two girls can complete the same work in 6 days. If each boy is paid 28 dollars per week, what should be the weekly wage of a girl, assuming wages are proportional to the work done?

Introduction / Context:
This question combines time and work concepts with proportional wage distribution. Given how quickly different combinations of boys and girls complete a work, we can infer their individual work rates. Since wages are proportional to work done in equal time, we then find how much a girl should earn compared with a boy whose weekly wage is known.

Given Data / Assumptions:
• Two boys and one girl finish the work in 5 days.
• One boy and two girls finish the same work in 6 days.
• Let the work rates of a boy and a girl be constant and independent.
• A boy is paid 28 dollars per week.
• Wages are proportional to work done for the same duration.

Concept / Approach:
We denote the daily work rate of a boy and a girl by variables and write equations for the total work in terms of these rates. Solving the system gives the ratio of work done by a boy and a girl in a day. Since wages are proportional to work done, the wage ratio equals this work ratio. Using the given weekly wage of a boy, we scale down to obtain the girl weekly wage.

Step-by-Step Solution:
Let b = work done by one boy in one day, and g = work done by one girl in one day. Total work is the same in both situations. From the first group: (2b + g) × 5 = 1 job, so 2b + g = 1 / 5. From the second group: (b + 2g) × 6 = 1 job, so b + 2g = 1 / 6. We now solve for b and g. Equations: 2b + g = 1 / 5 and b + 2g = 1 / 6. Multiply the first equation by 2: 4b + 2g = 2 / 5. Subtract the second: (4b + 2g) − (b + 2g) = 2 / 5 − 1 / 6. This gives 3b = 12 / 30 − 5 / 30 = 7 / 30, so b = 7 / 90. Substitute back into b + 2g = 1 / 6: 7 / 90 + 2g = 1 / 6. 1 / 6 = 15 / 90, so 2g = 15 / 90 − 7 / 90 = 8 / 90, giving g = 4 / 90 = 2 / 45. Ratio of work per day by boy to girl = b : g = (7 / 90) : (4 / 90) = 7 : 4. Hence wage ratio boy : girl = 7 : 4. If a boy earns 28 dollars, then 7 parts correspond to 28, so 1 part = 4 dollars and a girl earns 4 × 4 = 16 dollars.

Verification / Alternative check:
We can check by thinking in weekly work amounts. In a week, a boy does work proportional to 7 units and a girl to 4 units. If the boy earns 28 dollars, which is 7 units, then 1 unit is 4 dollars and 4 units give 16 dollars, confirming the calculation.

Why Other Options Are Wrong:
Values like 14, 22 or 24 dollars do not maintain the 7 : 4 wage ratio. For example, if the girl earned 14 dollars, the ratio 28 : 14 would be 2 : 1, not 7 : 4. Hence they are inconsistent with the work rate ratio derived from the equations.

Common Pitfalls:
Learners sometimes misinterpret the work completion times and incorrectly set up the equations, or they use the sums 5 and 6 directly in a ratio without recognizing the effect of the number of people. Another pitfall is to compare daily wages without ensuring that the time frame is the same for both workers.

Final Answer:
The weekly wage of a girl should be 16 dollars.