The 15% discount means that they only pay 100%-15% = 85% of the meal's bill.
This would cost 85% 78.65.
However, they also have to pay a 20% tip of the meal cost.
This would cost 20% 78.65.
Total Cost = (85% 78.65) + (20% 78.65)
= 105% 78.65
= 1.05 78.65
= $82.58