Question 1100600
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A father is 26 years older than his daughter. In 4 years, he will be 2 more than 5 times her age. Find out both their age. 
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<pre>
Let x be the father's age, y be the daughter age.

The condition gives you these two equations

x - y = 26,                 (1)      ("A father is 26 years older than his daughter")
x + 4 = 5*(y+4) + 2.        (2)      ("In 4 years, he will be 2 more than 5 times her age")


From eq(1), express  x = 26+y  and substitute it into eq(2). You will have


(26+y) + 4 = 5y + 20 + 2,

30 + y = 5y + 22  ====>  4y = 30-22 = 8  ====>  y = {{{8/4}}} = 2.


<U>Answer</U>.  The daugther is 2 years old, the father is 26 + 2 = 28 years old.


<U>Check</U>.   In 4 years, father will be 28+4 = 32 years old.

         The daughter will be 6 years old.

         6*5 +2 = 32.            ! Correct !
</pre>


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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.