SOLUTION: Hi The sum of Sofia and her mothers age is twice the difference between their ages. 5 years ago Sofia's mother is 4 times as old as Sofia. How old are they now. Thank you

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Question 1195175: Hi
The sum of Sofia and her mothers age is twice the difference between their ages. 5 years ago Sofia's mother is 4 times as old as Sofia. How old are they now.
Thank you
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Some of the wording is unclear. Taken as "mother WAS four times as old as Sofia":
d,m;
system%28d%2Bm=2%28m-d%29%2Cm-5=4%28d-5%29%29

-
d+m=2m-2d
2m-2d=d+m
m-3d=0
m=3d
-
m-5=4d-20
m=4d-15
-
3d=4d-15
0=d-15
0=3d-15
0=d-5
d=15
-
Daughter Sofia is 15, and her mother is 45.

Look for any mistakes, or possibly try the other interpretation for the description.

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Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hi
The sum of Sofia and her mothers age is twice the difference between their ages.
5 years ago Sofia's mother is 4 times as old as Sofia. How old are they now.
Thank you
~~~~~~~~~~~~~~~


            As  highlight%28usual%29,  the solution and the answer from the post of @josgarithmetic
            (5  years for daughter and  15  years for her mother)  are both  highlight%28WRONG%29  and  highlight%28INCORRECT%29.

            I came to bring you a correct solution. 


d,m;
system%28d%2Bm=2%28m-d%29%2Cm-5=4%28d-5%29%29


-
d+m = 2m-2d
2m-2d = d+m
m-3d = 0
m=3d
-
m-5=4d-20
m=4d-15
-
3d = 4d-15
0 = d-15
0 = d-15
d = 15
-
Sofia is 15 years old;  her mother is 45 years old.    ANSWER


You may check it on your own that all conditions of the problem are satisfied.

Solved.

----------------

For the safety of your brain,  ignore the post by @josgarithmetic.