Question

Billy is buying bows and name tattoo wrapping presents; he wants the same number of each. Bows come in packages of 4, and name tags are sold in packages of 6. What is the least number of bows and name tags that Billy can buy?

a) 12 bows and 18 name tags.
b) 16 bows and 24 name tags.
c) 24 bows and 24 name tags.
d) 8 bows and 8 name tags.

Answer 1

The least number of bows and name tags Billy can buy is found by calculating the least common multiple of 4 and 6, which is 24. Therefore, the correct answer is 24 bows and 24 name tags.

Step-by-step explanation:

To find the least number of bows and name tags Billy can buy with the same number, we need to look for the least common multiple (LCM) between the number of bows in a package, which is 4, and the number of name tags in a package, which is 6.

We are looking for the smallest number that both 4 and 6 can divide into without leaving a remainder.

Calculating the least common multiple of 4 and 6 involves listing the multiples of each number until we find a common one:

• Multiples of 4: 4, 8, 12, 16, 20, 24, ...
• Multiples of 6: 6, 12, 18, 24, 30, ...

We can see that 24 is the smallest multiple that both numbers share.

Therefore, Billy can buy 24 bows (which is 6 packages of 4) and 24 name tags (which is 4 packages of 6) to ensure that he has the same number of each item.

The correct answer is c) 24 bows and 24 name tags.