Question 1142250
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<pre>
Let D be the Dave age and C be the Christine's age.


Then you have these two equations


    C-5 = 5*(D-5)             (1)      ("5 years ago Christine's age was 5 times Dave's)

    D + 40 = 15 + {{{(C+40)/2}}}      (2)     ("In 40 years, Dave will be 15 years more than half Christine's age")



Multiply equation (2) by 2 (both sides).  You will get


    2D + 80 = 30 + C + 40.    (3)


Next express  C = 5*(D-5) + 5 from equation (1) and substitute it into equation (3). You will get


    2D + 80 = 30 + (5*(D-5) + 5) + 40.


Simplify and solve for D.


    2D + 80 = 30 + 5D - 25 + 5 + 40

    2D + 80 = 5D + 50

    80 - 50 = 5D - 2D

    30      = 3D

    D       = 30/3 = 10.


<U>ANSWER</U>.  Dave is 10 years old.  Christine is  C = 5*(D-5) + 5 = 5*(10-5) + 5 = 5*5 + 5 = 30 years old.
</pre>

You may check it &nbsp;ON &nbsp;YOUR &nbsp;OWN &nbsp;that my answer is correct.



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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> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/One-unusual-age-problem.lesson>One unusual age word problem</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/age/Age-problems-with-a-defective-sum-of-ages.lesson>Age problems with a defective sum of ages</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.