SOLUTION: The total ages of 3 people in a certain family is 75. The oldest is 35. Ten years ago the total of their ages was 47. How old is the youngest now? This is the problem, I tried m

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Question 1133054: The total ages of 3 people in a certain family is 75. The oldest is 35. Ten years ago the total of their ages was 47. How old is the youngest now?
This is the problem, I tried many solutions but all the time the result is 77. Can you please give me a clue? Thank you
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
PERSON       AGE NOW      TEN YEARS AGO
Youngest       y          y-10
Middle         m          m-10
Oldest         35         35-10=25
TOTAL          75         47


system%28y%2Bm=75-35%2C%28y-10%29%2B%28m-10%29%2B25=47%29

system%28y%2Bm=40%2Cy%2Bm=42%29
Not consistent.

Possible mistake either in my attempted solution, or faulty or incomplete problem description.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The condition in this problem describes  IMPOSSIBLE  situation,  which  NEVER  can happen
            - therefore  the problem  HAS  NO  solution.

            Indeed,  if the sum of ages of three persons today is  75,  then it can not be  47  ten years ago.

            Then years ago the sum of their ages is / (was)  75 - 3*10 = 75 - 30 = 45.


            In simple terms,  the condition is  INCORRECT.


===============

Added after reading the solution by tutor @MathTherapy. 

    Thanks for your solution and for correcting me.


    Now I recalled that I solved similar problem (even more than once) before at this forum.

    I even made a lesson  Age problems with a defective sum of ages  in this site with similar problem.


    But  I think that in such cases the condition should point by some gently and delicate manner to such a possibility.


    In the presented formulation the word "their" refers directly to "3 people" and is tooooo straightforward - and therefore incorrect.


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The total ages of 3 people in a certain family is 75. The oldest is 35. Ten years ago the total of their ages was 47. How old is the youngest now?
This is the problem, I tried many solutions but all the time the result is 77. Can you please give me a clue? Thank you 
It's possible, if the problem failed to disclose that 10 years ago, the youngest wasn't born. If that's incorrect and the youngest was alive, then it's impossible.



It's possible because the eldest is now 35, which means that he/she was 25 (35 - 10), 10 years ago.

At that time (10 years prior), the middle person was 22 (47 - 25), and is now 32 (22 + 10)

Therefore, with the youngest being Y, we get: 35 + 32 + Y = 75 

67 + Y = 75

Y, or youngest = highlight_green%28matrix%281%2C4%2C+75+-+67%2C+%22=%22%2C+8%2C+years-old%29%29

I agree, @IKLEYN. The word their, directly after itw's stated that the sum of the ages of the 3 is 75, suggests that the sum of "their" (the 3 individuals') ages,

10 years prior was 47. I do believe that "their" refers to the ages of the middle and older at that time. It's very AMBIGUOUS, but works if you treat it that way.