Middle School:
Question: Luke has 154 tulips and 105 daffodils. He wants to make the greatest number of bouquets that he can with the same number of tulips and the same number of daffodils in each, and he doesn't want to have any leftover flowers when he's done. How many tulips and how many daffodils should be in each bouquet?
Answer: 22 tulips and 15 daffodils
Solution: To solve this problem, we need to find the common factors of 154 and 105: 154 is divisible by 1, 2, 7, 11, 14, 22, 77, and 154, and 105 is divisible by 1, 3, 5, 7, 15, 21, 35, and 105. Their GCF is 7. So, the greatest number of bouquets with the same flowers in each that Luke can make is 7. If we divide the tulips among 7 bouquets, 22 go in each. If we divide the daffodils, 15 go in each.
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