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

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

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} = \frac{\text{ New number - Old number }}{\text{Old number }} * 100\, \%\\\\= (0.375x - 0.20x)/(0.20x) * 100\, \% = (0.175x)/(0.20x) * 100\, \% = 0.875 * 100\, \% = \mathbf{87.5 \, \%}\\\\\text{The number of biographies has increased by $\large \boxed{\mathbf{87.5 \, \%}}$}`