Question

Eve is making 50 gift baskets for the holidays. She wraps a red bow on every three baskets, a blue bow on every six baskets, and a gold bow on every eight baskets. Which baskets have all three bows?

Answer 1

Baskets number 24 and 48 will have all three bows — red, blue, and gold. We find this by identifying the least common multiple (LCM) of 6 and 8 within the range of 50 baskets, since the condition for the red bow is met by the blue bow condition.

Step-by-step explanation:

To find which baskets have all three bows, we need to determine a common number that is divisible by the numbers 3 (red bow), 6 (blue bow), and 8 (gold bow). Since every six baskets have a blue bow and every three baskets have a red bow, we can deduce that every basket with a blue bow also has a red bow, because 6 is a multiple of 3. Therefore, the red bow condition is already met by the blue bow condition. Now, we only need to find common multiples of 6 and 8 within the range of 50 baskets.

To find the least common multiple (LCM) of 6 and 8, we can list the multiples of each until we find a common one. Here are the multiples:

1. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
2. Multiples of 8: 8, 16, 24, 32, 40, 48, ...

The first common multiple within the range of 50 baskets is 24, followed by 48. Hence, baskets number 24 and 48 will have all three bows — red, blue, and gold.