Question 263784
A man spent 1/3 of his money and then lost 2/3 of the remainder. He was left with $12.00. How much did he start with? 


assume he $x

spent 1/3 *x

lost 2/3 *(x- 1/3*x)

x- (1/3  *x  + 2/3 * (x-1/3) *x)=12

x- (1/3*x +2/3(3x-x/3)) =12
x-(1/3 *x +4/9 *x)=12
x-((3x+4x) / 9)=12
9x-3x-4x=108
2x=108
x=54  He started with $ 54

spent 1/3 *x= $18

lost 2/3 *(x- 1/3*x) = 24

Balance =12