<PRE><B>Question 1149530</B>
&lt;br&gt;
The statement of the problem is faulty; it says now Antonette is older and 6 years ago her sister was older.&lt;br&gt;
I will ignore that and solve the problem as it was probably intended -- with Antonette older.&lt;br&gt;
Using formal algebra... which I will assume is what you are learning to do by asking this question....&lt;br&gt;
Let the sister&#39;s age be x
Then Antonette&#39;s age is x+3&lt;br&gt;
Then 6 years ago the sister&#39;s age was x-6, and Antonette&#39;s age was (x+3)-6 = x-3.&lt;br&gt;
Then, since 6 years ago Antonette was 4 times as old as her sister,&lt;br&gt;
{{{x-3 = 4(x-6)}}}
{{{x-3 = 4x-24}}}
{{{21 = 3x}}}
{{{x = 7}}}&lt;br&gt;
ANSWER: Antonette&#39;s age is x+3 = 10 years&lt;br&gt;
CHECK: 6 years ago, Antonette was 10-6 = 4 years old and her sister was 7-6 = 1 year old; Antonette was 4 times as old as her sister.&lt;br&gt;
Note that, if a formal algebraic solution is not required, the question can be answered quickly with a little logical reasoning and simple arithmetic.&lt;br&gt;
If the difference between their ages is 3 years, then when Antonette was 4 times as old as her sister, their ages had to be 4 and 1.&lt;br&gt;
And since that was 6 years ago, their ages now are 10 and 7.&lt;br&gt;
While knowing how to solve problems like this with formal algebra is important, solving them using logical reasoning is also good mental exercise.&lt;br&gt;
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