Question

Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased

Answer 1

Answer:

$\large \boxed{87.5 \, \%}$

Step-by-step explanation:

            Let x = the original number of books

Then 0.375x = the total number of biographies

 and 0.20  x = the original number of biographies

$\text{Percent increase} = \dfrac{\text{ New number - Old number }}{\text{Old number }} \times 100\, \%\\\\= \dfrac{0.375x - 0.20x}{0.20x} \times 100\, \% = \dfrac{0.175x}{0.20x} \times 100\, \% = 0.875 \times 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by \large \boxed{\mathbf{87.5 \, \%}} }$