Problem 8 · 2011 Math Kangaroo
Medium
Logic & Word Problems
caseworksum-constraint
Felix the Tomcat catches 12 fish in 3 days. On the second day he catches more than on the first. On the third day he catches more than on the second but less than on the first two days together. How many fish does he catch on day three?
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Answer: A — 5
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Hint 1 of 2
The three numbers add to 12 and increase, with day 3 less than the first two days combined.
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Hint 2 of 2
Try small increasing whole numbers that sum to 12 and check the day-3 condition.
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Approach: use the inequalities to pin the three day totals
- Let the catches be d1 < d2 on days 1 and 2, with total 12.
- Day 3 is more than day 2 but less than d1+d2.
- Testing d1=3, d2=4 gives d3=5: indeed 5>4 and 5<7, and 3+4+5=12.
- So on day three he catches 5 fish.
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