A certain man spent 10% of his life in childhood and 20% of his life as a young adult at which time he married his lovely bride. Five years later his son was born. His son lived to be half the age of his father when his father died. The man died ten years after his son died. How old was the man when he died? How old was the son when he died?
To find the age of the man when he died, let's break down the information given step by step:
1. The man spent 10% of his life in childhood: This means that 90% of his life was spent as an adult.
2. The man spent 20% of his life as a young adult before getting married: This means that 80% of his adult life remained after getting married.
3. Five years after getting married, his son was born.
4. His son lived to be half the age of his father when his father died: If the son lived to be half the age of his father, it means that the man's age when his son was born was twice the age of his son.
5. The man died ten years after his son died.
Let's assign variables to help us solve this problem:
- Let "M" represent the age of the man when he died.
- Let "S" represent the age of the son when he died.
Using the information above, we can create equations to solve for M and S:
1. The man spent 90% of his life as an adult: 0.9M
2. The man spent 80% of his adult life after getting married: (0.9M) * 0.8
3. The son was born 5 years after the man got married: (0.9M) * 0.8 - 5
4. The man's age when his son was born was twice the age of his son: (0.9M) * 0.8 - 5 = 2S
5. The man died ten years after his son died: M = S + 10
Now we have a system of equations to solve. We can substitute the value of M from equation 5 into equation 4:
(0.9M) * 0.8 - 5 = 2S
(0.9(S + 10)) * 0.8 - 5 = 2S
0.72S + 7.2 - 5 = 2S
0.72S = 2S - 2.2
0.28S = 2.2
S ≈ 7.86
So, the son was approximately 7.86 years old when he died. To find the age of the man, we can substitute this value back into equation 5:
M = S + 10
M = 7.86 + 10
M ≈ 17.86
Therefore, the man was approximately 17.86 years old when he died.
Let's break down the information we have step-by-step:
1. The man spent 10% of his life in childhood: Let's call the total lifespan of the man "x". Therefore, 0.1x represents the number of years he spent in childhood.
2. The man spent 20% of his life as a young adult: This means that 0.2x represents the number of years he spent as a young adult.
3. The man married his lovely bride after being a young adult for 0.2x years.
4. Five years later, his son was born. At this time, the man was 0.2x + 5 years old.
5. The son lived to be half the age of his father when his father died: If the father died at age "y", then the son lived to be (1/2)y years old.
6. The man died ten years after his son died: This means he lived for (1/2)y + 10 years.
From step 6, we can equate the lifespan of the man from steps 1 and 2 to find the value of x:
0.1x + 0.2x + 5 + (1/2)y = (1/2)y + 10
Combining like terms, we get:
0.3x + 5 = 10
Subtracting 5 from both sides, we have:
0.3x = 5
Dividing by 0.3, we find:
x = 16.67
This means the man's total lifespan was approximately 16.67 years.
Now, let's find the age of the man when he died:
Age of the man when he died = 0.2x + 5 + (1/2)y + 10
Substituting the value of x we found earlier, we have:
Age of the man when he died = 0.2(16.67) + 5 + (1/2)y + 10
Calculating this, we get:
Age of the man when he died ≈ 13.33 + 5 + (1/2)y + 10
Simplifying, we have:
Age of the man when he died ≈ 28.33 + (1/2)y
Since we don't know the age of the son when he died, we can't determine the exact age of the man when he died.
Therefore, based on the given information, we cannot determine the exact age of the man or his son when they died.