If the price is 15% higher than the purchase price, 20 yuan will make a profit, which means that 20 yuan accounts for 15% of the total purchase price, so the purchase price of all shoes is 20/ 15% = 400/3 yuan.

Then the price of each pair of shoes is = (400/3-64)/80 =13/15 yuan.

The purchase price of each pair of shoes = (13/15)/1.15 = 52/69 yuan.