SOLUTION: Helen is 54 years old. Her mom is 80 years old. How many years ago was Helen’s mom three times Helen’s age?

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Question 1114069: Helen is 54 years old. Her mom is 80 years old. How many years ago was Helen’s mom three times Helen’s age?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x years ago

3%2854-x%29=80-x
-
162-3x=80-x
162-80=2x
highlight%28x=41%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Informally....

The difference in their ages is 80-54 = 26 years.

When Helen's mother was three times as old as Helen, the difference in their ages was twice Helen's age. (3x-x = 2x)

2x=26 --> x=13; when Helen's mother was 3 times as old as Helen, Helen was 13.

Since Helen is now 54, that was 41 years ago.