Final answer:
The greatest number of identical bouquets without any leftover flowers that can be made from 15 tulips and carnations is 5, as it's the largest divisor of 15 that yields an integer result.
Step-by-step explanation:
The question asks to determine the greatest number of identical bouquets a florist can create without any leftover flowers, given that there are a total of 15 tulips and carnations. Since the question is concerned with dividing the flowers into equal groups, we need to find the largest divisor of 15 that would lead to an integer number of bouquets. The divisors of 15 are 1, 3, 5, and 15. Option (a) suggests 3 bouquets, option (b) suggests 5 bouquets, option (c) suggests 10 bouquets, and option (d) suggests 15 bouquets. Since 15 cannot be evenly divided by 10 without a remainder, option (c) is not possible. The greatest number of identical bouquets without leftovers, which is also the highest common factor among the options provided, is 5. Therefore, the correct answer is b) 5 bouquets.