One quantity stays the same

The ratio of comic books to storybooks on a shelf was 2 to 5. After 18 more comic books were added, the ratio became 4 to 5. How many storybooks are on the shelf? Try it first. Pause if you like. Draw what we know. Comic books, 2 blue units. Storybooks, 5 blue units. Before anything changes, look for the thing that stays the same. More comic books will arrive. But nobody touches the storybooks. That bar stays exactly as it is. We'll ring it and keep it in view. We'll need it. Now the 18 new comic books arrive. They join the comic book bar. These books are new, coming in from outside, so the new piece is purple. That piece is the 18. We don't know how many units it covers yet. And watch the storybooks. Nothing there changed. Let's line the two ratios up. Before, comic books to storybooks was 2 to 5. After, it's 4 to 5. Now look down the storybooks column. Nobody touched them. 5 before, and 5 after. The very same books. The same 5 blue units, before and after. So both ratios are counting in the same units. And that is what lets us compare this 2 with this 4. Now the comic books. The new ratio says 4, so the comic books are now 4 of those units. The first 2 are the blue ones we started with. The purple piece covers the other 2. So the 18 is exactly 2 units. So 2 units is 18. Then 1 unit is half of 18. That's 9. The storybooks are 5 units. 5 times 9 is 45. There are 45 storybooks. And you can see it on the shelf: 18 comic books, and 18 more, is 36. The storybooks never changed. That's what made the units match.