In the ancient kingdom of Eldoria, Pharaoh Thutmose III distributed a grand total of gold coins among his three royal advisors: Khepri, Isis, and Osiris. He decreed a peculiar condition: 'If Khepri had received double the coins he currently holds, Isis had received half the coins she currently holds, and Osiris had received three more coins than he currently holds, the total number of coins distributed would have remained exactly the same.' Given this, which of the following statements must be true regarding the original number of coins each advisor received?
Correct: The number of coins Khepri received was 3 less than half the number of coins Isis received.
Let K, I, and O represent the original number of coins Khepri, Isis, and Osiris received, respectively.
The initial total number of coins distributed is: Total_Original = K + I + O.
According to the pharaoh's condition, if Khepri had double (2K), Isis had half (I/2), and Osiris had three more (O+3), the total number of coins would remain the same.
So, Total_New = 2K + I/2 + (O + 3).
The core of the puzzle is that Total_Original = Total_New.
Therefore: K + I + O = 2K + I/2 + O + 3.
Now, let's simplify this algebraic equation:
1. Subtract K from both sides: I + O = K + I/2 + O + 3
2. Subtract O from both sides: I = K + I/2 + 3
3. Subtract I/2 from both sides: I - I/2 = K + 3
4. This simplifies to: I/2 = K + 3
5. Rearrange to solve for K: K = I/2 - 3.
This equation (K = I/2 - 3) or its rearrangement (I = 2K + 6) must be true.
Let's check the choices:
- Choice A: 'Isis received exactly three more coins than Khepri.' This means I = K + 3. This contradicts our derived relationship (I = 2K + 6).
- Choice B: 'The number of coins Khepri received was 3 less than half the number of coins Isis received.' This means K = I/2 - 3. This exactly matches our derived relationship. (Correct)
- Choice C: 'Khepri received exactly six more coins than Isis.' This means K = I + 6. This contradicts our derived relationship.
- Choice D: 'Osiris received three fewer coins than Khepri.' This means O = K - 3. The variable 'O' (Osiris's coins) cancelled out during our simplification (Total_Original = Total_New). This indicates that while Osiris's amount contributes to the overall total, his specific value does not impact the relationship between Khepri and Isis based *only* on the given condition. Therefore, we cannot determine a fixed relationship between O and K from the problem statement, so this statement is not necessarily true.