Fred is 3 years older than his sister Mary. In 7 years she will be of his age. How old are they now?

Let's denote Fred's current age as \( F \) and Mary's current age as \( M \).

We have two key pieces of information:
1. Fred is 3 years older than Mary, which gives us the equation: 
   \[
   F = M + 3
   \]
2. In 7 years, Mary will be of Fred's current age, which gives us the equation:
   \[
   M + 7 = F
   \]

Now, let's solve these equations step by step.

1. Substitute the first equation \( F = M + 3 \) into the second equation \( M + 7 = F \):
   \[
   M + 7 = M + 3
   \]

2. Simplify the equation:
   \[
   7 = 3
   \]

This result is impossible, indicating that no such ages exist that satisfy both conditions simultaneously.

Therefore, the problem as stated has no solution.

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Explore the solution to the problem where Fred is 3 years older than his sister Mary. In 7 years, Mary will be of Fred's current age. Discover the mathematical reasoning behind this age difference problem. Suitable for Grades 4-6.

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