one evening, three people play three rounds of a betting game with the undrestanding that the person who comes in last each round must double the money of the other two. After three rounds, each person has been last just once and each has $24. What were the three amounts at the start of the evening?
i tink its 2,4,12
is that correct?
39, 21,12
6, 42,24
12, 12, 48
24,24,24
To solve this problem, let's work backward and find the amounts at the start of the evening.
At the end of the third round, each person has $24. This means that after the doubling, each person had $12.
In the second round, the same must apply, as each person was last once. Since they end up with $12 each at the end of the second round, after the doubling, each person had $6.
Now, let's consider the first round. At the beginning of the game, each person had the same amount, which we will call "X". At the end of the first round, each person had $6.
According to the rules, the person who comes in last must double the money of the other two. Since each person ended up with $6, we can conclude that the person who came in last in the first round had $12 at the beginning.
Therefore, the amounts at the start of the evening were $12, $12, and $12.