Problem 25 · 2019 Math Kangaroo
Stretch
Fractions, Decimals & Percents
work-backward
Elisabeth has 60 pralines. On Monday she eats 110 of them. Of the ones left she eats 19 on Tuesday, then on Wednesday 18 of those left from the day before, on Thursday 17 of those left, and so on, until she eats one half of the pralines left over from the day before. How many pralines has she still got afterwards?
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Answer: E — 6
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Hint 1 of 2
Each day she removes a unit fraction of what is currently left.
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Hint 2 of 2
Track the running total day by day until the 'eat one half' step.
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Approach: apply each day's fraction in turn
- Start 60. Monday eat 1/10 → 54 left; Tuesday 1/9 → 48; Wednesday 1/8 → 42; Thursday 1/7 → 36.
- Continuing 1/6, 1/5, 1/4, 1/3, then 1/2 of what remains, the count drops to 30, 24, 18, 12, then 6.
- She has 6 pralines left.
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