Math Problem Statement
Fred is 3 years older than his sister Mary. In 7 years she will be of his age. How old are they now?
Solution
Let's denote Fred's current age as and Mary's current age as . According to the problem:
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Fred is 3 years older than Mary:
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In 7 years, Mary will be the same age that Fred is now:
Now, we can substitute the expression for from the first equation into the second equation:
Simplifying this:
Subtract from both sides:
This is a contradiction, indicating that something must be wrong. After revisiting the problem, I realize that the second statement should be: "In 7 years, Fred will still be 3 years older than Mary." Instead, the condition can be adjusted:
Updated condition:
In 7 years, Mary's age will be Fred's current age. So let's rewrite the system:
Plugging the first equation into the second:
Now, subtract from both sides:
This still does not seem right. I apologize for the mistake.
Correct Approach:
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Fred is 3 years older than Mary:
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In 7 years, Mary will be of Fred's current age:
Substituting into the second equation:
Now subtract from both sides:
Correct age substitution leads to:
Fred is 3 years older than Mary, so Fred's age .
And the current age difference should follow the equation:
Conclusion: Recalculating as above, the current age of Fred and Mary should simply equal:
.
If you have further doubts or questions, let me know!
Would you like more details or have any questions? Here are some related problems:
- If Fred were 5 years older than Mary, how would the equation change?
- What if Mary was younger by 4 years instead of 3?
- How do these age-related problems typically resolve when siblings age differently?
- What are typical age difference implications when siblings reach adulthood?
- Can there be any other formula that represents such age-related differences?
Tip: Always recheck conditions for specific clues or changes in the problem's statements.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 3-5