Final answer:
Dewayne should buy 3 packs of sodas and 5 packs of cupcakes to ensure each guest gets one soda and one cupcake, yielding 18 sodas and 20 cupcakes. The least common multiple of 4 and 6 is 12, but he must purchase whole packs, resulting in extras.
Step-by-step explanation:
The question is asking for the fewest number of cupcakes and sodas Dewayne must buy to have the same number of each, given that sodas are sold 6 to a pack and cupcakes are sold 4 to a pack. To solve this, you need to find the least common multiple (LCM) of the two numbers.
To start, list the multiples of each number:
- Multiples of 6: 6, 12, 18, 24, 30, ...
- Multiples of 4: 4, 8, 12, 16, 20, 24, ...
The smallest common multiple shared by both 4 and 6 is 12. Therefore, Dewayne must purchase enough packs to reach this common number. This means he will need to buy:
- 3 packs of sodas (6 sodas per pack x 3 packs = 18 sodas)
- 3 packs of cupcakes (4 cupcakes per pack x 3 packs = 12 cupcakes)
Since the question asks for an equal number of cupcakes and sodas, and he got 18 sodas, he needs to buy a total of 18 cupcakes as well, meaning he has to purchase 4.5 packs of cupcakes. However, since he can't buy half a pack, he will have to round up and purchase 5 packs of cupcakes to ensure there are enough. This will also leave him with a few extra cupcakes as a reserve.