Question 1169157
.
Timothy is 8 years older then his sister, in 5 years from now she will be half Timothy's age. How old is timothy and his sister now? 
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            This problem can be solved in several ways.


            I will show you two different ways to solve.




1.  &nbsp;&nbsp;<U>Two unknowns and two equations</U>


<pre>
Let x be the Timothy's age, an let y be the sister's age.


Then from the condition, you have these two equations
    
    x = y + 8        (1)

    x+5 = 2*(y+5)    (2)



Substitute into equation (2) this expression for x of equation (1). You will get

    y + 8 = 2*(y+5)



Simplify and find y

    y + 8 + 5  = 2y + 10

    8 + 5 - 10 = 2y - y

        3      = y.


Thus the sister's age is 3 years.


From equation (1), then  x = 3 + 8 = 11 is the Tymothy's age.


<U>ANSWER</U>.  Tymothy is 11 years old;  the sister is 3 years old.
</pre>


2. &nbsp;&nbsp;<U>Mental solution in your head without using equations</U>



<pre>
In 5 years, two events will happen simultaneously:


    Timothy will be 8 yeras older and two times as old as the sister.


    Hence, they will be  8 and 16 years old then.

    It means that now they are  8-5 = 3  and  16-5 = 11 years old.


You get the same answer</U>
</pre>


Solved two times to provide your better understanding.


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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=https://www.algebra.com/algebra/homework/word/age/02-HOW-TO-algebreze-and-solve-age-problems.lesson>HOW TO algebreze and to solve age problems?</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/Age-problem-for-3-participants.lesson>Age problem for three participants</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.