A library holds 12,000 titles, of which 3,000 are e-books. It plans to buy only e-books from now on and wants e-books to make up 40% of its holdings. How many e-books must it buy?

Every e-book bought lifts the top AND the bottom of the fraction, so write it out: $(3000+x)/(12000+x)=0.40$, giving $3000+x=4800+0.4x$, then $0.6x=1800$ and $x=3,000$. Check: 6,000 e-books out of 15,000 titles is exactly 40%. 1,800 is 4,800 - 3,000, the answer you get by holding the total at 12,000 - but the total moves too. 4,800 is 40% of the present holdings. 6,000 is the e-book count at the finish, not the number bought.