Why does the number of purines always equal the number of pyrimidines in a DNA strand

Because purines always base pair with pyrimidines and vice versa

Guanine, a purine, pairs with Cytosine, a pyrimidine and Adenine, a purine, pairs with thymine, a pyrimidine. Thus, if you have one strand of a DNA molecule, the corresponding molecule on the other strand will always be of the opposite type. This guarantees that the number of purines and pyrimidines are the same.

-Exandolon

Because of base pairings, a purine always pairs with a pyrimidine. Therefore, there must be one purine for each pyrimidine...