Work and Wages – Divide $450 among A, B, C by actual work done: A finishes in 10 days, B in 15 days; they work together for 5 days. C completes the remainder in 2 days. Split the $450 payment fairly.

Introduction / Context:
When workers contribute different fractions of the total job, payment should be split in direct proportion to the work each performs. We compute the work done by A and B in the joint period, determine the remainder, and assign it to C.

Given Data / Assumptions:

• A’s time = 10 days ⇒ rate = 1/10
• B’s time = 15 days ⇒ rate = 1/15
• They work together for 5 days
• C completes the rest in 2 days
• Total payment = $450

Concept / Approach:
Total work units are convenient; however, directly using fractions suffices. Joint daily rate of A and B is 1/10 + 1/15 = 1/6, so in 5 days they complete 5/6. The remaining 1/6 is done by C. Split $450 in the ratio 1/2 : 1/3 : 1/6 for A : B : C.

Step-by-Step Solution:
A’s share of work = 5 * (1/10) = 1/2B’s share of work = 5 * (1/15) = 1/3C’s share of work = 1/6Convert to parts: (3 : 2 : 1). Total parts = 6.Shares: A = 3/6 * 450 = $225; B = 2/6 * 450 = $150; C = 1/6 * 450 = $75

Verification / Alternative check:
Sum $225 + $150 + $75 = $450; fractions add to 1.

Why Other Options Are Wrong:
Other splits do not match the precise 3:2:1 ratio dictated by actual work.

Common Pitfalls:
Splitting only by rates without accounting for the different time each person actually worked.

Final Answer:
$225, $150, $75