Fred is three times older than his sister Mary. Four years ago he was five times as
old as his sister. Find their present ages

Let Fred's present age be denoted as \( F \) and Mary's present age as \( M \).

### Step 1: Create equations based on the problem statement
- **First condition**: Fred is three times older than Mary. This gives us the equation:
  \[
  F = 3M
  \]

- **Second condition**: Four years ago, Fred was five times as old as Mary. This translates to:
  \[
  F - 4 = 5(M - 4)
  \]

### Step 2: Solve the system of equations
#### Substitution method:
1. From the first equation, \( F = 3M \), substitute this into the second equation:
   \[
   3M - 4 = 5(M - 4)
   \]
2. Simplify the second equation:
   \[
   3M - 4 = 5M - 20
   \]
3. Rearrange the terms:
   \[
   3M - 5M = -20 + 4
   \]
   \[
   -2M = -16
   \]
4. Solve for \( M

Fred is three times older than his sister Mary. Four years ago he was five times as old as his sister. Find their present ages.

Discover how to solve this algebraic age problem: Fred is three times older than his sister Mary, and four years ago, he was five times her age. Learn how to set up and solve the system of equations step-by-step, suitable for students in Grades 6-8.

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