Keats Library purchases a number of new books, all in the ca

Let C = the current number of books and B = the number of added biographies.

C = 20% biographies.
B = 100% biographies.
The MIXTURE of C and B = 37.5% biographies.

To determine the required ratio of C to B, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for C and B on the ends and the percentage for the mixture in the middle.
C 20%---------------37.5%---------------100% B

Step 2: Calculate the distances between the percentages.
C 20%-----17.5-----37.5%-----62.5-----100% B

Step 3: Determine the ratio in the mixture.
The ratio of C to B is equal to the RECIPROCAL of the distances in red.
\(\frac{C}{B}\) = \(\frac{62.5}{17.5}\)= \(\frac{125}{35}\) = \(\frac{25}{7}\)= \(\frac{100}{28}\).

The resulting ratio implies that the number of biographies must increase by 28 if there are currently 100 books.
Since 20% of these 100 books would be biographies -- implying a present tally of 20 biographies -- we get:
\(\frac{increase-in-biographies}{current-number-of-biographies}\)= \(\frac{28}{20}\) = \(\frac{140}{100}\) = 140%.