Question 1151041
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<pre>

Let x be the age of the car (in months), and

let y be the age of the tires (in months, again).


When the car was as old as the tires are now ?  --- Obviously, (x-y) months ago.



So, according to the first part of the condition

    x = 3*(y - (x-y)).


Simplify it:


    x = 3*(2y-x)  

    x = 6y - 3x

    x + 3x = 6y

    4x = 6y

    2x = 3y.           (1)


When the car's tires will be as old as the car is now ?  ----  In (x-y) months, obviously.


So, according to the second part of the condition,

    x + (x-y) = y + 12    months.


Simplify it:


    2x - y = y + 12,

    2x - 2y = 12.      (2)



From equation (1), substitute 2x = 3y into equation (2), replacing 2x by 3y there.  You will get then


    3y - 2y = 12,

     y      = 12.


Thus, the tires current age is 12 months.


Then from (1),  2x = 3y = 3*12 = 36;  hence,  x = 36/2 = 18.


<U>ANSWER</U>.  The car is 18 months old.  The tires are 12 months old.
</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> 

in this site.


Read them and become an expert in solving age problems.


Of these lessons, &nbsp;for the most close problems to yours in this post, &nbsp;is the lesson marked &nbsp;(*) &nbsp;in the list.


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.