Problem 4 · 2020 Math Kangaroo
Medium
Algebra & Patterns
sum-constraintcasework
Every night the wizard Tilim makes the weather forecast for the king. When Tilim gets it right he gets 3 gold coins, but when he makes a mistake he pays a fine of 2 gold coins. After making the prediction for 5 days, Tilim found that he neither won nor lost coins. How many times did he get the weather forecast right in those 5 days?
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Answer: C — 2
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Hint 1 of 2
The coins he wins must exactly cancel the coins he pays in fines.
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Hint 2 of 2
Try a few guesses: how many right days make the coins won equal the coins lost?
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Approach: make the coins won match the coins lost
- He ends with no change, so the coins he won must equal the coins he paid.
- Each right day wins 3 coins and each wrong day costs 2 coins, over 5 days.
- If he was right 2 days: 2 × 3 = 6 coins won, and the other 3 days cost 3 × 2 = 6 coins.
- 6 won and 6 paid balance out, so he was right 2 times.
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