Adam put all of his pencils in his bookbag. The next day, he gave away 5 of them to his friends to use in class. Later that week, half of his pencils were broken at the bottom of his bag. He now has 12. How many pencils did he start with?

Adam started with a total of 24 pencils. By doubling the number of unbroken pencils he was left with (12), we find that he originally had 24 pencils before any were given away or broken.

Explanation:

Adam started with 24 pencils. First, let us consider the information provided: after giving away 5 pencils and later finding that half of his pencils were broken, he now has 12 pencils. Since these 12 pencils represent the half that was not broken, we can calculate the original number by doubling the current amount.

Adam currently has 12 unbroken pencils, which is half of his original amount.
Therefore, the total amount before any were broken is 12 (the unbroken half) multiplied by 2, giving us 24 pencils.
Since he had given away 5 before this count, we include those to find the original total. However, since the 5 given away were included in the original total before any were broken, we can confirm that Adam started with 24 pencils.