Question 1101153
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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.<br>
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.<br>
So the statement of the problem should say that Claire's mother is 4 times AS OLD AS Claire -- not 4 times older.<br>
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<br>
Then since the sum of the ages is 57,
{{{x + x+3 + 4x = 57}}}
{{{6x+3 = 57}}}
{{{6x = 54}}}
{{{x = 9}}}<br>
The brother's age is 9+3 = 12.