Question 1089455
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<pre>
The correct system of equations is

M - 2 = 7*(D - 2),   (1)
M + 3 = 4*(D + 3).   (2)

Simplify this system:

M - 2 = 7D - 14      (1')
M + 3 = 4D + 12      (2')

M = 7D - 12,         (1'')
M = 4D +  9,         (2'')

====> 7D - 12 = 4D + 9  ====>  7D - 4D = 9 + 12  ====>  3D = 21  ===>  D = 7.


Daughter is 7 years old now. The mother is (from (2'')) M = 4D + 9 = 4*7 + 9 = 28 + 9 = 37.


<U>Answer</U>.  The mother is 37 years now.
</pre>

Solved.



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>

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>".



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The solution by @josgarithmetic is <U>WRONG</U>.


For your safety, simply ignore it.