Problem 2 · 2012 AMC 8
Easy
Ratios, Rates & Proportions
unit-rate
In the country of East Westmore, statisticians estimate there is a baby born every 8 hours and a death every day. To the nearest hundred, how many people are added to the population of East Westmore each year?
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Answer: B — About 700.
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Hint 1 of 2
Births and deaths are quoted on different clocks (every 8 hours vs. every day). Find a single day's net change first — then a year is just many copies of that day.
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Hint 2 of 2
This is find the per-day net, then scale: get one clean daily number, multiply by 365. Don't track births and deaths separately all the way out.
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Approach: net change per day, then scale to a year
- Put both on a one-day clock: a birth every 8 hours means 24 / 8 = 3 births a day, against 1 death a day.
- Net per day = 3 − 1 = 2 people. (Working with the net now means one multiplication later, not two.)
- Over a year: 2 × 365 = 730, which rounds to 700.
- Sanity check: ≈2 a day for a year should be in the high hundreds — 700 fits, 70 or 7000 would not.
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