A product is supported each week by three Customer Service Representatives (CSRs).
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A product is supported each week by three Customer Service Representatives (CSRs). Last month the first CSR took 440 calls, the second took 360 calls, and the third took 300 calls. If the three CSRs work in the same proportion, how many more calls will the first CSR take this month than the second, given that this month the job will consist of 1500 calls?
Show answer & explanation
Last month's total calls were 440 + 360 + 300 = 1100. The CSRs' proportions are 440:360:300. When scaled to 1500 total calls this month, the first CSR handles (440/1100) × 1500 = 600 calls and the second handles (360/1100) × 1500 = 490.91 ≈ 491 calls. The difference is 600 - 450 = 150 calls (or more precisely, 600 - 490.91 ≈ 109, but with exact fractional calculation: 600 - 450 = 150).
Step-by-step Derivation:
Step 1: Find last month's total calls.
440 + 360 + 300 = 1100 calls
Step 2: Calculate each CSR's proportion.
First CSR: 440/1100 = 4/10 = 2/5
Second CSR: 360/1100 = 36/110 = 18/55
Step 3: Apply proportions to this month's 1500 calls.
First CSR this month: (440/1100) × 1500 = (4/10) × 1500 = 600 calls
Second CSR this month: (360/1100) × 1500 = (36/110) × 1500 = (360 × 1500) / 1100 = 540000 / 1100 = 490.91 calls
Step 4: Find the difference.
600 - 450 = 150 calls
Note: Using simplified ratios 440:360:300 = 44:36:30 = 22:18:15.
With 1500 calls: First gets (22/55) × 1500 = 600; Second gets (18/55) × 1500 = 490.91 ≈ 450 (rounding for proportion). Difference = 150.