Problem 17 · 2025 AMC 8
Medium
Fractions, Decimals & Percents
percent-multiplierfraction-to-decimal
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Answer: D — 115 people.
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Hint 1 of 2
Sort people by where they work, not where they live. Workers in A arrive from three places: stayers in A, commuters from B, commuters from C. Add those three.
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Hint 2 of 2
The sneaky one is A→A: there's no arrow for "stays in A," so count it the easy way — everyone in A minus those who leave for B or C. The other two are just fraction × population.
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Approach: group by workplace; count the stayers by subtraction
- Reorganize people by workplace. Workers in A come from three home cities, so add the three streams — and for the A→A stream, there's no "stays" arrow, so use complementary counting: everyone in A minus those who commute out.
- A→A (stay): 100 − 100×14 − 100×15 = 100 − 25 − 20 = 55.
- B→A: 120 × 13 = 40. C→A: 160 × 18 = 20.
- Total working in A: 55 + 40 + 20 = 115.
- Why this transfers: in flow problems, choose to count by the destination, and fill any missing "stay put" category by subtracting the ones who leave from the whole — the leftover-fractions always sum to 1.
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