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The difference in the age between two friend is 12years.8years ago, the elder friend was twice as old as the young friend.what are the current ages?
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The difference in the age between two friend is 12years.8years ago, th...
Understanding the Problem
To find the current ages of the two friends, we need to set up equations based on the information provided:
- The difference in age is 12 years.
- Eight years ago, the elder friend was twice as old as the younger friend.
Setting Up the Variables
- Let the current age of the younger friend be \( y \).
- Therefore, the current age of the elder friend will be \( y + 12 \).
Creating the Equations
1. Age Difference Equation:
- \( \text{Elder} - \text{Younger} = 12 \)
- \( (y + 12) - y = 12 \) (This confirms the age difference)
2. Age Comparison Equation (8 years ago):
- Eight years ago, the ages would have been:
- Younger friend: \( y - 8 \)
- Elder friend: \( (y + 12) - 8 = y + 4 \)
- According to the problem, the elder friend was twice the age of the younger friend at that time:
- \( y + 4 = 2(y - 8) \)
Simplifying the Equation
- Expanding the equation:
- \( y + 4 = 2y - 16 \)
- Rearranging gives:
- \( 4 + 16 = 2y - y \)
- \( 20 = y \)
Finding Current Ages
- The younger friend's current age \( y \) is 20 years.
- The elder friend's current age is \( y + 12 = 20 + 12 = 32 \) years.
Conclusion
- The current ages of the friends are:
- Younger Friend: 20 years
- Elder Friend: 32 years
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The difference in the age between two friend is 12years.8years ago, the elder friend was twice as old as the young friend.what are the current ages?
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