Question 1132111
.


<U>The solution using two variables and two equations</U>


<pre>
Let x be the Bon's age and let y be the Sonia's (his daughter's) age.


From one side, we have this equation 

x - y = 25            (1)    ("Sonia is 25 years younger than her father".)



From the other side, we have second equation

x + 10 = 2*(y+10)     (2)    (in 10 years . . . )


So, we have the system of equations (1) and (2) in two unknowns.

To solve it, express  x = 25 + y  from eq(1), and substitute it into equation (2). You will get

(25 + y) + 10 = 2*(y+10)

35 + y = 2y + 20

35 - 20 = 2y - y

15 = y.


Thus Sonia is 15 years old now.

Hence, the father is  x = 25 + y = 25 + 15 = 40 years old.


<U>Answer</U>.  Sonia is 15 years old;  the father is 40 years old.
</pre>

Solved.



<U>The solution using one variable and single equation</U>


<pre>
Let x be the Sonia's age.

Then the Bon's age is  (x+25), according to the condition.


In 10 years Sonia's age will be (x+10) years,  while Bon's age will be (x+25)+10 = (x+35).


Then the condition says

x + 35 = 2*(x+10).


It implies

x + 35 = 2x + 20

35 - 20 = 2x - x

15 = x.


And you get THE SAME ANSWER.
</pre>

The second solution is completed.


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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.