SOLUTION: Six years age, 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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Question 1110796: Six years age, 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?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

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Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
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Six years ago, 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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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 =  = 14.


Then  r = 4*14-18 = 38.


Answer.  d = 14,  r = 38.

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There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
    - Age problems for mental solution
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
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".


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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Be aware: The solution by @josgarithmetic and his answer   d = 14   and   r = 46   are   W R O N G.



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