SOLUTION: Khalid loses 1|3th of his money in the first game, 3.5th of the remainder in the second and 4|7th of the rest in third. Then he is left with .........th of money?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Khalid loses 1|3th of his money in the first game, 3.5th of the remainder in the second and 4|7th of the rest in third. Then he is left with .........th of money?       Log On


   

Question 1112868: Khalid loses 1|3th of his money in the first game, 3.5th of the remainder in the second and 4|7th of the rest in third. Then he is left with .........th of money?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x equal the original amount of money that he started with.

he starts the first game with x.
he loses 1/3 of the money that he started the first game with.
that means he loses 1/3 * x.

the money he has left after the first game is x - 1/3 * x.
simplify to get:
the money he has left after the first game is 2/3 * x.

he starts the second game with 2/3 * x.
he loses 3/5 of the money that he started the second game with.
that means he loses 3/5 * 2/3 * x.

the money he has left after the second game is 2/3 * x - 3/5 * 2/3 * x.
simplify this to get:
the money he has left after the second game is 2/3 * x - 6/15 * x.

put everything under the common denominator of 15 and you get:
the money he has left after the second game is 10/15 * x - 6/15 * x.
simplify to get:
the money he has left after the second game is 4/15 * x.

he starts the third game with 4/15 * x.
he loses 4/7 of the money that he started the third game with.
that means he loses 4/7 * 4/15 * x.

the money he has left after the third game is 4/15 * x - 4/7 * 4/15 * x.
simplify this to get:
the money he has left after the third game is 4/15 * x - 16/105 * x.

put everything under the common denominator of 105 and you get:
the money he has left after the third game is 28/105 * x - 16/105 * x.
simplify this to get:
the money he has left after the third game is 12/105 * x
simplify this further to get:
the money he has left after the third game is 4/35 * x.

that's your solution.

the money he has left after the third game is 4/35th of the money that he started out with.