An elderly gentleman passes on. He leaves half of his estate to his wife. He leaves his son $50,000. The remainder of the money is divided as follows: He leaves half of the remaining money to his best friend. He then leaves half of what is now remaining to his church. He donates the remaining $8,000 to the local elementary school for research and implementation of Constructivist learning theory in mathematics education. How much money was originally in this gentleman’s estate?
Let X be the amount the gentleman originally had in his estate.
He leaves half his estate, X/2, to his wife, so there is X/2 remaining.
The son receives $50,000, so there is (X/2) - 50,000 remaining.
The best friend receives half of what is remaining, so the church receives (X/2 - 50,000)/2 = (X/4 - 25,000).
The church receives half of what is remaining, so the school receives (X/4 - 25,000)/2 = (X/8 - 12,500).
He donates $8,000 to the school, so X/8 - 12,500 = 8,000.
Adding 12,500 to both sides, X/8 = 20,500.
Multiplying both sides by 8, the final equation is X = $164,000. Answer: \boxed{164,000}.
To determine the original amount of money in the gentleman's estate, we will work backwards.
Let's assume the original amount in the estate is represented by the variable X.
According to the information given:
- Half of the estate, which is X/2, is left to the wife.
- $50,000 is left to the son.
- The remaining money after leaving $50,000 to the son is X - $50,000.
- Half of the remaining money, which is (X - $50,000)/2, is left to the best friend.
- After giving half of the remaining money to the best friend, the amount left is (X - $50,000)/2 - (X - $50,000)/2 = 0.
- Half of what is now remaining, which is 0/2 = 0, is left to the church.
- Finally, the remaining $8,000 is donated to the elementary school.
From this, we can form the equation:
(X/2) + $50,000 + [(X - $50,000)/2] + 0 + $8,000 = X
Now we can solve this equation to find the value of X:
(X/2) + (X - $50,000)/2 + $8,000 = X
Multiplying each term by 2 to get rid of the denominators:
X + X - $50,000 + $16,000 = 2X
Combining like terms:
2X - X = $50,000 - $16,000
X = $34,000
Therefore, the original amount of money in the gentleman's estate was $34,000.
To determine the original amount in the gentleman's estate, we need to work backwards from the information provided.
Let's break down the given information step by step:
1. The gentleman leaves half of his estate to his wife. This means the remaining amount is also half of the original estate.
2. He leaves his son $50,000. So, the son receives a fixed amount that is separate from the estate, and we don't need to consider it when calculating the original estate amount.
3. The remainder of the money (after leaving $50,000 for the son) is divided as follows: half to his best friend, and half of what is now remaining to his church.
4. After giving half to his best friend, half of what remains is given to the church. This implies that the remaining amount is again divided in half.
5. Finally, he donates the remaining $8,000 to the local elementary school.
Let's work through the calculations step by step:
Let's say the original estate amount is X.
Step 1: After leaving half to his wife, the remaining amount is X/2.
Step 2: After giving his son $50,000, the remaining amount is (X/2 - $50,000).
Step 3: After giving half to his best friend, the remaining amount is [(X/2 - $50,000)/2].
Step 4: After giving half of what remains to the church, the remaining amount is [(X/2 - $50,000)/2 - (X/4 - $25,000)].
Step 5: Finally, after donating $8,000 to the school, the remaining amount is [(X/2 - $50,000)/2 - (X/4 - $25,000) - $8,000].
According to the given information, this remaining amount is $0.
Therefore, we can set up the equation:
[(X/2 - $50,000)/2 - (X/4 - $25,000) - $8,000] = $0
Now, we can solve for X:
[(X/2 - $50,000)/2 - (X/4 - $25,000)] = $8,000
By simplifying and solving this equation, we can find the original amount in the gentleman's estate.