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