We can rewrite 3:4 as 3x:4x since we don't know the actual individual numbers, solely that it is divisible by these numbers.
Next, since we know 3x = 36 because of the question, we can solve for x using the division property of equality and get x=12. Once we have x=12 we can find the number of books the other trader has - 4x - by simply multiplying 12 by 4 to get 48 books. Now all we need to do is find the total number of books that both traders have and to do this all we need to do is add 36 to 48 to get a final answer of 84 books.
First, factor the expression on the top. What two numbers add to get 8 and multiply to 15? 5 and 3! so the top expression factors to (x+3)(x+5). You can cancel the x+3 from the denominator and end up with x+5. Make sense?
