Monika’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
6 years
Understanding the Age Difference Problem
This problem involves calculating the age difference between Monika's parents based on their ages when their children were born.
Analyzing the Given Information
We are given two key pieces of information:
- Monika's father was 38 years old when Monika was born.
- Monika's mother was 36 years old when Monika's brother was born.
- Monika's brother is four years younger than Monika.
We need to find the difference between the ages of Monika's parents.
Setting up Age Relationships
Let's denote the current ages:
- Monika's current age as $M$ years.
- Monika's brother's current age as $B$ years.
- Monika's father's current age as $F$ years.
- Monika's mother's current age as $Mo$ years.
From the first statement, when Monika was born, her age was 0. Her father's age was 38. This means the father is always 38 years older than Monika. So, we can write the relationship:
$\qquad F = M + 38$
From the third statement, Monika's brother is 4 years younger than Monika. This means Monika is 4 years older than her brother. So, we can write the relationship:
$\qquad B = M - 4$
From the second statement, when Monika's brother was born, his age was 0. His mother's age was 36. This means the mother is always 36 years older than the brother. So, we can write the relationship:
$\qquad Mo = B + 36$
Calculating the Age Difference Between Parents
We want to find the difference between the ages of her parents, which is $F - Mo$.
We have the equations:
1. $F = M + 38$
2. $B = M - 4$
3. $Mo = B + 36$
We can substitute the value of $B$ from equation (2) into equation (3):
$\qquad Mo = (M - 4) + 36$
$\qquad Mo = M - 4 + 36$
$\qquad Mo = M + 32$
Now we have the ages of the father and mother in terms of Monika's age $M$:
$\qquad F = M + 38$
$\qquad Mo = M + 32$
To find the difference between their ages, we subtract $Mo$ from $F$:
$\qquad F - Mo = (M + 38) - (M + 32)$
$\qquad F - Mo = M + 38 - M - 32$
$\qquad F - Mo = 38 - 32$
$\qquad F - Mo = 6$
The difference between the ages of Monika's parents is 6 years.
| Relationship | Equation | Explanation |
|---|---|---|
| Father's age vs Monika's age | $F = M + 38$ | Father is 38 years older than Monika. |
| Brother's age vs Monika's age | $B = M - 4$ | Brother is 4 years younger than Monika. |
| Mother's age vs Brother's age | $Mo = B + 36$ | Mother is 36 years older than the brother. |
| Mother's age vs Monika's age (Substitution) | $Mo = (M - 4) + 36 = M + 32$ | Substituting brother's age in terms of Monika's age. |
| Difference between Parents' ages | $(M + 38) - (M + 32)$ | Subtracting Mother's age from Father's age. |
The calculation shows that the difference is a constant value (6 years) and does not depend on the current age of Monika ($M$).
Conclusion on Parents' Age Difference
Based on the calculations, the difference between the ages of Monika's father and mother is 6 years.
Revision Table: Age Difference Problem
| Concept | Key Idea | Application in Problem |
|---|---|---|
| Age Relationship | Difference in age between two people remains constant over time. | Father is always 38 years older than Monika. Mother is always 36 years older than brother. |
| Relative Ages | Expressing one person's age in terms of another's. | Brother's age = Monika's age - 4. |
| Substitution | Replacing a variable with its equivalent expression. | Substituting brother's age expression into the mother-brother age equation. |
| Solving for Difference | Subtracting the expressions for the two quantities. | Subtracting the expression for Mother's age from the expression for Father's age. |
Additional Information: Solving Age Word Problems
Age word problems often require setting up algebraic equations based on the relationships given in the problem. Here are some tips:
- Identify the unknown ages you need to find or relate. Use variables to represent them.
- Translate the given statements into mathematical equations. Pay attention to phrases like "years older," "years younger," "times as old," etc.
- Remember that the difference in age between two people remains constant throughout their lives.
- If the problem talks about ages at different points in time (e.g., "5 years ago," "10 years from now"), express the ages at those times in terms of the current age variable.
- Solve the system of equations to find the unknown values or the required difference.
In this specific problem, the core idea is that the age difference between any two individuals stays constant. By relating both parents' ages to one of the children's ages (via substitution), we could directly find the difference between the parents' ages without needing to know anyone's exact current age.
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