Solving the Age Word Problem
Let the daughter's current age be d years and the man's current age be m years.
Setting Up Age Equations
From the first statement, "A man is 4 times as old as his daughter", we get the first equation:
$m = 4d \quad (1)$
In 20 years, the daughter will be d + 20 years old, and the man will be m + 20 years old. The second statement, "In 20 years, he will be twice as old as she will be then", gives us the second equation:
$m + 20 = 2(d + 20) \quad (2)$
Solving for Daughter's Current Age
Substitute the value of m from equation (1) into equation (2):
$4d + 20 = 2(d + 20)$
Distribute the 2 on the right side:
$4d + 20 = 2d + 40$
Subtract 2d from both sides:
$4d - 2d + 20 = 40$
$2d + 20 = 40$
Subtract 20 from both sides:
$2d = 40 - 20$
$2d = 20$
Divide by 2:
$d = \frac{20}{2}$
$d = 10$
The daughter's current age is 10 years.
Verification
If the daughter is 10 years old now, the man is $4 \times 10 = 40$ years old.
In 20 years:
- Daughter's age will be $10 + 20 = 30$ years.
- Man's age will be $40 + 20 = 60$ years.
Check if the man is twice as old as the daughter then: $60 = 2 \times 30$. This is true.
Therefore, the daughter's current age is 10 years.
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