So, you want to get the mixed number, 3 3/4, as a fraction. Multiply 3 by 4 and add it to the top of the fraction, getting you the fraction 15/4. Multiply the top and bottom by 2, getting the denominator to 8 and the numerator to 30. Now, you have two fractions, 30/8 and 3/8, with common denominators. Divide 30 by 3, you get 10. 10 books for the first part. Using this explanation you'll find that the new shelf can hold 14 books.
What you have to do is add them all! 20 bar 11.4 2 11.4 weights 11.4 4.5 2 4.5 weights 4.5 450.0 4 450 weights 450.0 450.0 +450.0 --------- 1.8 10 200 +1,600 -------------- 1,811.8 is the answer