Question

Bill and Sam go to a casino. They each have the same amour of money. After an hour bill had won $20 and Sam lost the same amount. The next hour bill had lost two thirds of all his money and Sam had won the same amount. At that point Sam had four times as much as bill. How much money did they each have before they started?

Answer 1

They each have $180 before they started.

Explanation:

Let x represents the amount they each have before they started. Therefore, we have:

Amount with Bill after one hour = x + $20

Amount with Sam after one hour = x - $20

Amount with Bill after two hours = (x + $20) - (x + $20)(2 / 3)

Amount with Sam after two hours = (x - $20) + (x - $20)(2 / 3) = 4((x + $20) - (x + $20)(2 / 3)) ............... (1)

From equation (1), we can solve for x as follows:

(x - $20) + (x - $20)(2 / 3) = 4((x + $20) - (x + $20)(2 / 3))

(x - $20) + (x - $20)0.666666666666667= 4((x + $20) - (x + $20) 0.666666666666667)

x - $20 + 0.666666666666667x - $13.3333333333333= 4(x + $20 - 0.666666666666667x - $13.3333333333333)

x - $20 + 0.666666666666667x - $13.3333333333333= 4x + $80 - 2.66666666666667x - $ 53.3333333333332

Collecting the like terms, we have:

x + 0.666666666666667x - 4x + 2.66666666666667x = $80 - $53.3333333333332+ $20 + $13.3333333333333

(1 + 0.666666666666667- 4 + 2.66666666666667)x = $60

0.333333333333337x = $60

x = $60 / 0.333333333333337

x = $180

Therefore, they each have $180 before they started.