SOLUTION: Hi Sam Raj and Caleb had 144 coins altogether. When Sam gave some coins to Raj the number of coins Raj had doubled. Raj then gave some of his coins to Caleb and Caleb coins also d

Question 1193510: Hi
Sam Raj and Caleb had 144 coins altogether. When Sam gave some coins to Raj the number of coins Raj had doubled. Raj then gave some of his coins to Caleb and Caleb coins also doubled. If the 3 had the same number of coins at the end, how many did each have.
Thanks
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

There are 144 coins total and we don't introduce any new coins to the system when any of the exchanges happen.
The phrase "3 had the same number of coins at the end" tells us that each person has 144/3 = 48 coins when both exchanges are done.

Focus on "Raj then gave some of his coins to Caleb and Caleb coins also doubled." which is the second exchange that happens. We'll be following the exchanges in reverse until we reach the initial state.

Since Caleb's coin count doubles after Raj hands some over, this means Caleb's count of 48 was originally 48/2 = 24 coins. Caleb gained 24 coins to get 24+24 = 48 total.

This means Raj handed over 24 coins.
Raj must have had 48+24 = 72 coins before handing over those 24 coins (since 72-24 = 48) to Caleb.

Now refer to "Sam gave some coins to Raj the number of coins Raj had doubled. " and we play the same type of game as the previous paragraph.
If Raj's count doubled, and he landed on 72, then he started with 72/2 = 36 coins.
Raj gained 36 coins to get 36+36 = 72 total.
Therefore, Sam handed over 36 coins and Raj started with 36 coins.

Sam ends up with 48 coins and he handed over 36.
Sam must have started with 48+36 = 84 coins

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Let's summarize:
Sam started with 84 coins
Raj started with 36 coins
Caleb started with 24 coins

Notice that
84+36+24 = 144
which helps to partially confirm the answer

Now let's focus on the first exchange. Sam hands over 36 coins to Raj
Sam ends up with 84-36 = 48 coins
Raj now has 36+36 = 72 coins

Now onto the second exchange
Raj gives 24 coins to Caleb
Raj ends up with 72-24 = 48 coins
Caleb ends up with 24+24 = 48 coins

Each person ends up with 48 coins. The answer has been fully confirmed at this point.

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Answer:
The starting coin counts are
Sam = 84 coins
Raj = 36 coins
Caleb = 24 coins

Extra info:
Sam gave 36 coins to Raj
Raj gave 24 coins to Caleb

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