Hadley loves to do volunteer work at the local library. On a certain day, she neatly arranges 100 books on the shelf. By lunchtime, a certain number of books had been borrowed. She added 40 more books to the same shelf. By evening, 30 more books had been borrowed. If the shelf had 60 books remaining by the evening, how many books had been borrowed by lunchtime?
Thoughts? Step-by-step reasoning:
Let x be the number of books borrowed by lunchtime. So by lunchtime, the remaining number of books will be 100 - x. After adding 40 more books, the total number of books increased to 100 - x + 40. By evening, after 30 more books have been borrowed, the total number of books remaining is 100 - x + 40 - 30 = 60. Thus 110 - x = 60. Thus x = 50 books.
Thus, the answer is 50.