Total Money: x
Amount spent; 2/3 (x)
Amount lost: 2/3 (1/3)(x) or 2/9 (x)
Amount left after spending and losing part of money: 200
Equation:
x = 2/3 (x) + 2/9 (x) + 200
Multiply each term by LCD 9:
(9) x = (9) (2/3) (x) + (9) (2/9) (x) + 200 (9)
9x = 6x + 2x + 1,800
9x = 8x + 1,800
9x - 8x = 1,800
x = 1,800
ANSWER: The woman had Php 1,800.
Check:
Amount spent: 2/3 (1,800) = 1,200
Amount lost: 2/9 (1,800) = 400
Amount left = 200
Add:
1,200 + 400 + 200 = 1,800
1,800 = 1,800 (True)