<PRE><B>Question 1153882</B>
.


&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;Since the equation is written &amp;nbsp;INCORRECTLY &amp;nbsp;in the post by @josgarithmetic,

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;I came to bring a correct Algebra solution.



&lt;pre&gt;
Let sister&#39;s age be x; then Ben&#39;s age is (x-6).


In 10 years, their ages are (x+10)  and  ((x-6)+10).


So, the equation for the total age in 10 years is


    (x+10) + ((x-6)+10) = 50.


Simplify and solve


    2x + 14 = 50

    2x      = 50 - 14 = 36.

     x                = 36/2 = 18.


&lt;U&gt;ANSWER&lt;/U&gt;.  The sister is 18 years old.  Ben is 18-6 = 12 years old.
&lt;/pre&gt;

Solved.


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There is a bunch of lessons on age word problems 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/word/age/Age-problems-and-their-solutions.lesson&gt;Age problems and their solutions&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/word/age/Fresh-formulation-of-a-traditional-age-problem.lesson&gt;A fresh formulation of a traditional age problem&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson&gt;Really intricate age word problems&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/age/Selected-age-word-problems-from-the-archive.lesson&gt;Selected age word problems from the archive&lt;/A&gt;

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problems-for-mental-solution.lesson&gt;Age problems for mental solution&lt;/A&gt; 

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/word/age/Miscellaneous-age-problem.lesson&gt;Miscellaneous age problems&lt;/A&gt; 

in this site.


Read them and become an expert in solving age problems.


Also, &amp;nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;- &lt;A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson&gt;ALGEBRA-I - YOUR ONLINE TEXTBOOK&lt;/A&gt;.


The referred lessons are the part of this online textbook under the topic &quot;&lt;U&gt;Age word problems&lt;/U&gt;&quot;.



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.


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