Subjects algebra

Gamblers Start F59B82

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1. **State the problem:** A gambler starts with an unknown amount of money $x$. After a series of bets and winnings, we want to find the original amount $x$. 2. **Define variables and write equations:** - After the first race, he doubled his money: amount = $2x$. - He bets $33$ on the second race and triples the money he came with (which is $2x$), so after the second race: amount = $3(2x) = 6x$. - He bets $60$ on the third race and quadruples his original bankroll $x$, so after the third race: amount = $4x$. - He bets $68$ on the fourth race and loses it, but still has $64$ left. 3. **Set up the equation for the fourth race:** The amount before the fourth race minus the bet $68$ equals $64$: $$4x - 68 = 64$$ 4. **Solve for $x$:** $$4x - 68 = 64$$ Add $68$ to both sides: $$4x = 64 + 68$$ $$4x = 132$$ Divide both sides by $4$: $$\cancel{4}x = \cancel{4}33$$ $$x = 33$$ 5. **Interpretation:** The gambler started with $33$. **Final answer:** $33$