Problem 22 · 2022 Math Kangaroo
Stretch
Algebra & Patterns
substitution
Five girls eat plums. Laura eats 2 more plums than Sophie. Bettina eats 3 fewer plums than Laura. Clara eats one more plum than Bettina, and 3 fewer than Alice. Which two girls eat the same number of plums?
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Answer: E — Clara and Sophie
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Hint 1 of 3
Pretend Sophie eats some easy number of plums, like 10, then work out everyone else from the clues.
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Hint 2 of 3
Go in order: Laura is 2 more than Sophie, Bettina is 3 less than Laura, Clara is 1 more than Bettina.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you have all five numbers, look for two girls with the same count.
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Approach: pretend Sophie's number, then fill in the rest
- Say Sophie eats 10 plums (any number works the same way).
- Laura eats 2 more, so 12; Bettina eats 3 less than Laura, so 9; Clara eats 1 more than Bettina, so 10; Alice eats 3 more than Clara, so 13.
- Now compare: Sophie has 10 and Clara has 10 — they match!
- So the two girls who eat the same are Clara and Sophie (choice E).
For older kids (with letters)
Let Sophie = S. Then Laura = S+2, Bettina = S−1, Clara = S, Alice = S+3, so Clara = Sophie.
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