Question 1101089
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Three years ago, Evan was one third of his sister's age. In a year's time, Evan's age doubled will match his sister's age. How old is Evan now?
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<pre>
Let y be Evan's age, and

let x be the sister's age.



From the condition, you have these two equations

y - 3 = {{{(1/3)*(x-3)}}},      (1)    ("Three years ago, Evan was one third of his sister's age.")

2*(y+1) = x + 1.      (2)     ("In a year's time, Evan's age doubled will match his sister's age.")



From eq(1),  3*(y-3) = x - 3  ====>  3y - 9 = x - 3  ====>  x = 3y - 6.

Now substitute it into eq(2). You will get

2*(y+1) = (3y-6) + 1  ====>  2y + 2 = 3y - 5  ====>  y = 2 + 5 = 7.



<U>Answer</U>.  Evan is 7 years old.  His sister is 15 years old (from eq(2)).
</pre>

Solved.


The solution by @josgarithmetic  ("y = 10 Evan now") is &nbsp;&nbsp;<U>W R O N G </U>.



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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 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.