Question

Boxes of pencils are sold in packs of 12 and pens are sold in packs of 8. If you want to buy the same number of pencils and pens. What is the least number of pencils and pens that you would need to buy? How many packs of pencils will you need to buy? How many packs of pens would you need to buy?

A) You need to buy 12 pencils and 12 pens. You need to buy 1 pack of pencils and 1 pack of pens.
B) You need to buy 24 pencils and 16 pens. You need to buy 2 packs of pencils and 2 packs of pens.
C) You need to buy 8 pencils and 12 pens. You need to buy 1 pack of pencils and 2 packs of pens.
D) You need to buy 18 pencils and 24 pens. You need to buy 1 pack of pencils and 3 packs of pens.

Answer 1

The least common multiple of 12 and 8 is 24. Therefore, to have the same number of pencils and pens, one would need to buy 2 packs of pencils and 3 packs of pens to get 24 each.

Step-by-step explanation:

When trying to find the least number of pencils and pens you would need to buy when boxes of pencils are sold in packs of 12 and pens are sold in packs of 8, you need to find the least common multiple (LCM) of 12 and 8. The LCM of 12 and 8 is 24, which means you would need to buy at least 24 pencils and 24 pens. As pencils come in packs of 12, you would need 2 packs of pencils. For pens, which come in packs of 8, you would require 3 packs of pens to get 24 pens.

To buy the same number of pencils and pens, the least number you need to buy is 24 of each. Therefore, you would need 2 packs of pencils and 3 packs of pens. The correct option is:

B) You need to buy 24 pencils and 24 pens. You need to buy 2 packs of pencils and 3 packs of pens.