SOLUTION: Sam was twice the square of Jon's age plus another four times Jon's age when Helen was the square of Jon's age plus 45. Sam and Helen are twins.At this moment in time, how old was

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Question 1136473: Sam was twice the square of Jon's age plus another four times Jon's age when Helen was the square of Jon's age plus 45. Sam and Helen are twins.At this moment in time, how old was Sam?




Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
Sam    = 2*((Jon)^2 ) + 4*Jon.    (1)    ("Sam was twice the square of Jon's age plus another four times Jon's age")

Helen  =     Jon^2 + 45           (2)    (Second condition).


Since Sam and Helen are twins, their ages are the same; hence, right sides of equations (1) and (2) are equal:


    2*J^2 + 4J = J^2 + 45,    or


    J^2 + 4J - 45 = 0,

    (J-5)*(J+9) = 0.


Only positive root is meaningful:  J = 5.


Hence, Sam = 2*J^2 + 4*J = 2*5^2 + 4*5 = 2*25 + 20 = 50 + 20 = 70.


ANSWER.  Sam is 70 years old.

You can check my answer on your own by calculating the Helen's age.



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


At some point in time, when Jon's age was x, Sam's age was 2x^2+4x, and Helen's age was x^2+45; and Sam and Helen are the same age. At THAT point in time, then,




or

Clearly a negative age makes no sense, so at THAT point in time, Jon was 5; that means Sam and Helen were each 70.

But I don't know how to answer the question, because it is badly worded.

If the actual question is "at THAT moment in time, how old WAS Sam", then the answer is clearly 70.

But if the actual question is "at THIS point in time (i.e., now), how old IS Sam", there is no information given that allows us to determine that -- except that it would have to be more than 70, since Sam WAS 70 at some time in the past.

But we don't now how to answer the question, because the question that is asked sloppily asks "at THIS point in time, how old WAS Sam?"
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