Difficulty: Medium
Correct Answer: 131 calls
Explanation:
Introduction / Context:
This question tests understanding of proportional increase when workloads scale up while preserving the same relative distribution between workers. The situation comes from a customer support or product support context, where three supporters handle calls. When the total number of calls changes, their individual loads change proportionally, and the goal is to focus specifically on how much extra work the second supporter will do in the new month compared to the previous month.
Given Data / Assumptions:
- Last month calls handled: first supporter 440, second supporter 360, third supporter 300.
- Total calls last month = 440 + 360 + 300 = 1,100 calls.
- Total calls this month are planned at 1,500 calls.
- Work is divided in the same ratio as earlier among the three supporters.
- We need the increase in the number of calls for the second supporter only.
Concept / Approach:
If workloads increase while keeping relative contributions constant, each person’s share is scaled by the same factor. The scaling factor is new total calls divided by old total calls. Once that factor is known, we multiply the second supporter’s old workload by this factor to get the new workload. The difference between the new workload and the original workload gives the additional number of calls for the second supporter.
Step-by-Step Solution:
Step 1: Compute last month total calls = 440 + 360 + 300 = 1,100.
Step 2: Compute the scaling factor = new total / old total = 1,500 / 1,100 = 15 / 11.
Step 3: Second supporter old workload = 360 calls.
Step 4: Second supporter new workload = 360 * (15 / 11).
Step 5: Calculate 360 * 15 / 11 = 5,400 / 11 which is approximately 490.9 calls.
Step 6: Since calls are discrete, we interpret this as about 491 calls in practice.
Step 7: Increase in calls for the second supporter = 491 minus 360 = 131 calls.
Verification / Alternative check:
We can check proportionality by computing how many calls the other supporters would get with the same factor 15 / 11 and see whether the total comes close to 1,500. The first supporter would get 440 * 15 / 11, and the third would get 300 * 15 / 11. Summing the approximate values together gives a total near 1,500, showing the scaling factor is used correctly. Slight rounding to the nearest whole call is acceptable in such word problems where call counts must be integers.
Why Other Options Are Wrong:
160 calls and 600 calls represent much larger increases than justified by the scaling factor. They would give the second supporter a workload that is not consistent with proportional division. The value 491 calls is close to the new workload, but the question asks for the increase in calls, not the total. Therefore, 491 is not the correct final response; instead we need the difference which is 131.
Common Pitfalls:
Learners often confuse total new workload with the increment and mistakenly select a value near 491 instead of computing the increase above 360. Another pitfall is recalculating a completely new ratio instead of scaling the old distribution. Forgetting to compute the scaling factor from total calls can also lead to arbitrary or incorrect allocations among supporters.
Final Answer:
The second supporter will handle an additional 131 calls this month compared to last month.
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