Problem 24 · 2025 Math Kangaroo
Stretch
Counting & Probability
caseworkcareful-counting
Zita would like to buy some flowers. She can choose between flowers for 3€, 4€ and 5€. How many different bouquets can she buy for exactly 23€?
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Answer: D — 7
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Hint 1 of 2
Count how many flowers of each price (3, 4, 5 euro) add up to exactly 23 euro.
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Hint 2 of 2
Systematically vary the number of 5-euro flowers, then fill the rest with 3s and 4s.
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Approach: count whole-number combinations summing to 23
- We need non-negative whole numbers a, b, c with 3a + 4b + 5c = 23.
- Step through the number of 5-euro flowers and, for each, the 4-euro flowers, checking the rest is a multiple of 3.
- Listing them gives exactly 7 different bouquets.
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