Name: rham
Who is asking: Student
Level: Middle

Question:
Bill and Sam went off to bet at the casino. Each started with the same number of dollars. At the end of the first hour, Bill had won 20$ and sam had lost 20$. At the end of the second hour, BIll had lost two thirds of his money, and Sam had won the same amount that Bill had lost. At that point, sam had four times as much money as BIll. How much did each one start with?

Hi Rham
Suppose that they each started with $D. At the end of the first hour Bill had $(D+20) and Sam had $(D-20). The next statement is somewhat confusing. I am going to read this as "DURING the second hour BIll lost two thirds of his money, and Sam won the same amount that Bill lost". That is during the second hour Bill lost two thirds of the $(D+20) he had at the end of the first hour. With this interpretation at the end of the second hour Bill has $(D+20)-2/3(D+20) and Sam has $(D-20)+2/3(D+20). Since you know that at this time Sam has four times the money that Bill has, (D-20)+2/3(D+20)=4[(D+20)-2/3(D+20)]. Now solve for D

Cheers,
Penny