Question 1147611
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will try to provide &nbsp;<U>more short solution</U>.



<pre>
Let x be the Matt's age.   Then James' age is 90-x years.


When Matt will be twice as old as James is now ?

    - In   2*(90-x)-x  years, which is 180-3x years.


What will be the James' age in 180-3x years ?

    - James age will be  (90-x) + (180-3x), or, after simplifying,  (270-4x) years.


Then the condition says

    x = {{{(1/2)*(270 - 4x)}}}


<U>It is your basic equation to the problem</U>.   Now your task is to solve it.


    2x  = 270 - 4x

    6x  = 270

    x   = 270/6 = 45.


<U>ANSWER</U>.  Matt is 45 years old.  James is 90-45 = 45 years old, too.


<U>CHECK</U>.   When Matt will be twice as old as James is now (i.e. as old as 2*45 = 90 years ?

             - In  90-45 = 45 years.

         What will be James' age in 45 years ?

             - it will be  45 + 45 = 90.


          45 = {{{90/2}}}.   ! Correct !         
</pre>

Solved.


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In such problems, &nbsp;than shorter, &nbsp;compact and straightforward &nbsp;the solution is, &nbsp;than more &nbsp;(and better) &nbsp;it is understandable.



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In this site, &nbsp;there is a bunch of 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 problem</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/One-unusual-age-problem.lesson>One unusual age word problem</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problems-with-a-defective-sum-of-ages.lesson>Age problems with a defective sum of ages</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/04-OVERVIEW-of-lessons-on-age-problems.lesson>OVERVIEW of lessons on age problems</A>


Of them, &nbsp;the problem marked (*) in the list is very close to the given problem.


Read the lessons 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.