<human>:  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?
<bot>: Define a variable ** Let x be the number of books borrowed by lunchtime.
How many books are remaining? ** So by lunchtime, the remaining number of books will be 100-x
How many books are remaining after adding 40 more books? ** After adding 40 more books, the total number of books increased to 100-x+40.
How many books are remaining by evening? ** By evening, after 30 more books have been borrowed, the total number of books remaining is 100-x+40-30 = 60
Write an equation ** Thus 110 - x = 60.
Divide by 10 ** Thus x = <<50=50>>50 books
#### 50