Three numbers sum to 172. The first-to-second ratio is 8:11, and the second-to-third is 5:7. Find the second number.
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Answer: B. 55
Explanation
Combining the given ratios of eight to eleven and five to seven produces a unified three-part ratio of forty to fifty-five to seventy-seven. The sum of all ratio parts equals forty plus fifty-five plus seventy-seven, which totals one hundred seventy-two parts. Multiplying the second person proportional share fraction by the total sum of one hundred seventy-two gives an exact value of fifty-five. Combined ratios allow multiple quantities to be compared across a single unified proportional scale. Proportional distribution divides a total given amount among participants based on their respective fractional ratio shares. Finding a common scaling factor bridges separate ratio pairs into a single continuous proportional sequence.
Option A suggests forty-four, which corresponds to an incorrect ratio share allocation from the combined sequence. Option C proposes sixty-six, failing to match the proportional share derived from the unified ratio parts. Option D offers seventy-seven, which represents the third partner's share rather than the second partner's share.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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