Question 1110796
.
Six years {{{highlight(cross(age))}}} <U>ago</U>, Rosa was four times as old as her daughter. Ten years from now, she will be only twice as old as her daughter. 

How old are they now?
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<pre>
r-6 = 4(d-6),        (1)
r + 10 = 2*(d+10)    (2)


From (1), express r = 4*(d-6) + 6 = 4d - 24 + 6 = 4d -18  and substitute it into (2). You will get


4d - 18 + 10 = 2*(d+10),

4d - 8 = 2d + 20  ====>  2d = 20+8 = 28  ====>  d = {{{28/2}}} = 14.


Then  r = 4*14-18 = 38.


<U>Answer</U>.  d = 14,  r = 38.
</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.



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<U>Be aware</U>:  The solution by @josgarithmetic and his answer  &nbsp;&nbsp;d = 14  &nbsp;&nbsp;and &nbsp;&nbsp;r = 46  &nbsp;&nbsp;are &nbsp;&nbsp;<U>W R O N G</U>.