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8.3.10 Dave is playing blackjack at his local casino. He starts with $1,000 and on each hand he bets 50% of his money. If he wins a hand, then he wins whatever he bet, but if he loses a hand, then he loses whatever he bet. After playing 5 hands, he has won 3 hands and has lost 2 hands. How much money does Dave have after the 5 hands? Does it matter which 3 of the 5 hands he won?
Hint: It's often best to think of percent increases and decreases in terms of multiplying the original quantity by some number.
Hint: Suppose Dave has $x before betting half his money on a hand. How much will he have if he wins? How much will he have if he loses?

Respuesta :

Answer:

The amount Dave got after 3 wins and 2 loose is $843.75. The order of win and loose doesn't matter.

Step-by-step explanation:

- We are given with a word problem

- We are asked to find the amount he had after 5 hands

- We can do this in two steps

Step 1 : Identifying the percentages

Step 2 : Finding the amount left

Step 1 of 2

We are given with a word problem. He bets 50% of his money. If he wins he get his bet, if he loose he will loose the money too. If he wins he will get the money as 150%.

That is, 1.5

If he loose he will loose money by 50%

That is, 0.50

Step 2 of 2

The amount got after 5 hands with 3 wins and 2 loose is,

[tex]$\begin{gathered}1000 \times(1.5)^{3} \times(0.5)^{2}=1000 \times 3.375 \times 0.25 \\1000 \times 0.84375=843.75\end{gathered}$[/tex]
3 wins 2 looses 843.75

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