A woman spent two third of her money. She lost two-third of the remainder and then had 200 pesos left. With how much money did he start?
Let x = starting money
x - 2/3x - 2/3(1/3x) = 200
Solve for x.
To solve this problem, we need to work through it step by step.
Let's assume the woman's starting amount of money is "x" pesos.
According to the problem, she spent two-thirds of her money, which means she has one-third left. So, the remaining amount of money after spending is (1/3)x pesos.
Next, the problem states that she lost two-thirds of the remainder. This means she has (1 - 2/3) or 1/3 remaining from the previous amount. So, the expression for her final amount of money is (1/3) * (1/3)x pesos.
According to the problem, she ends up with 200 pesos. So we can equate the expression for her final amount to 200:
(1/3) * (1/3)x = 200
To solve for x, we can multiply both sides of the equation by 9 to cancel out the fractions:
(1/3) * (1/3)x * 9 = 200 * 9
(1/3) * x = 1800
Now, we can solve for x by multiplying both sides of the equation by 3:
x = 1800 * 3
x = 5400
Therefore, the woman started with 5400 pesos.