Question 1123149
.
<U>Formal solution</U>


<pre>
T = J + 12         (1)       ("Ted is 12 years older than Juan.")

T + 1 = 3*(J+1)    (2)       ("Next year ted will be 3 times as old as Juan.")


From eq(1), substitute the expression for T into eq(2), replacing T. You will get


(J + 12) + 1 = 3*(J+1),

J + 13 = 3J + 3

13 - 3 = 3J - J

10 = 2J   ====>  J = 10/2 = 5.


<U>Answer</U>.  Juan is 5 years old.


<U>Check</U>.  Ted is 5+12 = 17 years old.

        Next year  Juan will be 6 years old;  Ted will be 18 years old, i.e. three times Juan's age then.

        ! Correct !
</pre>


<U>Logic solution</U>


<pre>
Next your Ted will be 3 times Juan's age and 12 years older than Juan.


Hence (apply your logic skills !),  Tedd will be 18, while Juan will be 6.


It means that Juan is 5 years old now, while Ted is 17 years old.
</pre>


Solved by two different ways giving the same result.


--------------------


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 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> 

in this site.


Read them and become an expert in solving age problems.


Also, 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.