Question

Sign 4 Billy is buying bows and name tags for wrapping Christmas presents. He wants the same number of each. Bows come in packages of 9. Name tags are sold in packages of 6. What is the least number of bows and name tags that Billy can buy?

A) 15 bows and 9 name tags
B) 18 bows and 6 name tags
C) 24 bows and 12 name tags
D) 27 bows and 27 name tags
Decide if each statement about 8 and 12 is true or false. Choose True or False for each statement.
Statement 1: 8 is a multiple of 12. True / False
Statement 2: 12 is a multiple of 8. True / False
Statement 3: 8 and 12 are both prime numbers. True / False
Statement 4: The sum of 8 and 12 is 20. True / False

Answer 1

Billy can buy the least number of bows and name tags by finding the least common multiple (LCM) of 9 and 6, which is 18 bows and 18 name tags.

Step-by-step explanation:

Billy wants to buy the same number of bows and name tags. Bows come in packages of 9 and name tags come in packages of 6. In order to find the least number of bows and name tags that Billy can buy, we need to find the least common multiple (LCM) of 9 and 6.

The prime factorization of 9 is 3 x 3, and the prime factorization of 6 is 2 x 3. To find the LCM, we need to take the highest power of each prime factor that appears in either factorization. So the LCM of 9 and 6 is 2 x 3 x 3, which is 18.

Therefore, the least number of bows and name tags that Billy can buy is 18 bows and 18 name tags, which corresponds to option B) 18 bows and 6 name tags.