Sam’s mother is twice as old as Sam. In 12 years, Sam will be as old as his mother was 12 years ago. How old are Sam and his mother now?
The Correct Answer and Explanation is:
Step 1: Define the Variables
Let:
- Sam’s current age be S
- His mother’s current age be 2S (since she is twice as old as Sam)
Step 2: Use the Information Given
“In 12 years, Sam will be as old as his mother was 12 years ago.”
- Sam’s age in 12 years = S + 12
- His mother’s age 12 years ago = 2S – 12
So we create the equation: S+12=2S−12S + 12 = 2S – 12
Step 3: Solve the Equation
S+12=2S−1212+12=2S−S24=SS + 12 = 2S – 12 \\ 12 + 12 = 2S – S \\ 24 = S
So Sam is 24 years old, and his mother is: 2×24=48 years old2 \times 24 = 48 \text{ years old}
✅ Final Answer:
Sam is 24 years old. His mother is 48 years old.
300-word Explanation (RDW format: Read, Draw, Write)
Read:
The problem says Sam’s mother is twice as old as Sam. It also says that in 12 years, Sam will be as old as his mother was 12 years ago. This tells us we are comparing ages across different time points. The best way to solve this is by using algebra to create an equation that reflects these relationships.
Draw (or Visualize):
Let’s call Sam’s age “S.” Since his mother is twice his age, her age is “2S.” In 12 years, Sam will be S + 12, and his mom’s age 12 years ago was 2S – 12. The problem says these two ages will be equal: S+12=2S−12S + 12 = 2S – 12
Solving this:
Subtract S from both sides: 12=S−1212 = S – 12
Add 12 to both sides: 24=S24 = S
That means Sam is 24. His mother is twice that: 48. We can check this:
- In 12 years, Sam will be 36.
- 12 years ago, his mother was 36.
Perfect match!
Write:
We found Sam is 24 years old and his mother is 48 years old. We used algebra to set up the relationship between their ages, using the clue about future and past ages. Solving the equation showed that the relationship checks out, confirming our answer is correct.
