Paiva Corporation owns $80\%$ of Ackroyd Corporation's outstanding common stock and Ackroyd owns $80\%$ of the outstanding common stock of Bailey Corporation. Bailey Corporation owns $10\%$ of the outstanding common stock of Ackroyd Corporation. The cost of the investments was equal to book value and there were not fair value$/$book value differences for the investments. The separate net incomes for the three affiliated companies for the year ended December $31,2014($excluding investment income$)$ are as follows: Paiva Corporation, $$100,000,$ Ackroyd Corporation, $$50,000,$ and Bailey Corporation, $$30,000.$ Use the conventional approach.

Symbols used:

P $=$ Income of Paiva on a consolidated basis

A $=$ Income of Ackroyd on a consolidated basis

B $=$ Income of Bailey on a consolidated basis

The equation, in a set of simultaneous equations, that computes Paiva Corporation income on a consolidated basis is