Question

Bonzo went to a carnival. At the first

Answer 1

Bonzo started with 2.1 dollars

Step-by-step explanation:

Assume that Bonzo has $x

1. Change $x to cents

2. Calculate the remaining money with him after each game

3. Equate the left money in the 3rd game by zero to find x

∵ $1 = 100 cents

∴ $x = 100 x cents

First game

∵ Bonzo has 100 x cents

∵ He paid 10¢ to get in

∴ The money left is (100 x - 10)

∵ He spent half  the money he had left

- That mean the money left with him is the other have

∴ The money left with him = $\frac{1}{2}$ (100 x - 10) = (50 x - 5) cents

∵ He spent 10¢  to get out

∴ The money left after 1st game = (50 x - 5) - 10

∴ The money left after 1st game = (50 x - 15) cents

Second game

∵ Bonzo has (50 x - 15) cents

∵ He paid 10¢ to get in

∴ The money left is (50 x - 15) - 10 = (50 x - 25)

∵ He spent half  the money he had left

∴ The money left with him = $\frac{1}{2}$ (50 x - 25) = (25 x - 12.5) cents

∵ He spent 10¢  to get out

∴ The money left after 2nd game = (25 x - 12.5) - 10

∴ The money left after 2nd game = (25 x - 22.5) cents

Third game

∵ Bonzo has (25 x - 22.5) cents

∵ He paid 10¢ to get in

∴ The money left is (25 x - 22.5) - 10 = (25 x - 32.5)

∵ He spent half  the money he had left

∴ The money left with him = $\frac{1}{2}$ (25 x - 32.5) = (12.5 x - 16.25) cents

∵ He spent 10¢  to get out

∴ The money left after 3rd game = (12.5 x - 16.25) - 10

∴ The money left after 3rd game = (12.5 x - 26.25) cents

∵ He found he had no money left after the 3rd game

∴ Equate the left money with him by zero

∴ 12.5 x - 26.25 = 0

- Add 26.25 to both sides

∴ 12.5 x = 26.25

- Divide both sides by 12.5

∴ x = 2.1

Bonzo started with 2.1 dollars

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