SOLUTION: Claire's brother is 3 years older than her. Her mother is 4 times older than her. Their combined age is 57. By constructing an equation, calculate how old her brother is

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Question 1101153: Claire's brother is 3 years older than her. Her mother is 4 times older than her. Their combined age is 57. By constructing an equation, calculate how old her brother is
Found 2 solutions by greenestamps, Alan3354:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


With the problem as stated, there is no solution, because the ages all turn out to be mixed numbers. Age problems should have solutions that are positive integers.

The difficulty is in the statement that Claire's mother is 4 times older than Claire. "4 times older than x" means x, plus x 4 more times, or 5x. But trying to solve the problem that way gives ages that are not whole numbers.

So the statement of the problem should say that Claire's mother is 4 times AS OLD AS Claire -- not 4 times older.

Once we have gotten past the incorrect statement of the problem, we have
x = Claire's age
x+3 = her brother's age
4x = her mother's age

Then since the sum of the ages is 57,
x+%2B+x%2B3+%2B+4x+=+57
6x%2B3+=+57
6x+=+54
x+=+9

The brother's age is 9+3 = 12.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It seems the authors of math problems don't know the difference between "4 times older" and "4 times as old." I suggest they get a different job.
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I've seen "10 times closer." What can that mean? 1 time closer --> no distance between the objects.
And "10 times smaller."
Ignorance is rampant.
Avoid it.