Question 1164417
.
Faith is 10 years older than Grace. Eight years ago, Faith was 3 times Grace's age. How old are they now?
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<pre>
Let x be the Grace age;  Then Faith is (x+10) years old.


Eight years ago they were  (x-8) (Grace)  and  ((x+10)-8) = (x+2)  (Faight) years old.


The condition says


    x+2 = 3*(x-8).


From this equation


    x+2 = 3x - 24

    2 + 24 = 3x - x

    26     = 2x

     x     = 26/2 = 13.


<U>ANSWER</U>.  Grace is 13 years old;  Faith is 13+10 = 23 years old.


<U>CHECK</U>.  8 years age they were  13-8 = 5  and  23-8 = 15 years old with the ratio {{{15/5}}} = 3.  ! Correct !
</pre>

Solved.


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There is a bunch of lessons on age word problems 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Age-problems-and-their-solutions.lesson>Age problems and their solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Fresh-formulation-of-a-traditional-age-problem.lesson>A fresh formulation of a traditional age problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/age/Really-intricate-age-word-problem.lesson>Really intricate age word problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Selected-age-word-problems-from-the-archive.lesson>Selected age word problems from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problems-for-mental-solution.lesson>Age problems for mental solution</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Miscellaneous-age-problem.lesson>Miscellaneous age problems</A> 

in this site.


Read them and become an expert in solving age problems.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Age word problems</U>".



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.