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A woman spent two-thirds of her money.She lost two-thirds of the remainder and then had 200 pesos left.How much money did she start ?

Sagot :

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)