Question 144256: john is 3 times the age his son will be next year. his wife is 20 years older than her son is this year. there combined ages total 71. how old is each person.
this is a puzzle which my father and i cant agree on. we are both mathamatically minded but disagree about the answer. he says it must be possible to answer using algebra and came up with ,john 31, wife 30 and son 10. my point is in the first sentence (sons age +1)x 3 he worked on the basis (sons age x 3) +1, here we disagree. i have tried various routes to the answer assuming there is some sort of trickery in the wording but cannot find an answer other than (son 9 now therefore could be 11 at some point next year) (therefore dad could be 33)(mother 20 years older than son is this year could be 9+20=29)therefore totalling 71. i would be dissapointed if there were no logical mathamatical answer and that it just word trickery. i would rather be wrong than dissapointed.
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! I agree that the question is poorly worded, making it somewhat ambiguous
__ it seems that the author is trying to imply son's age plus 1
let x="son this year"
"john is 3 times the age his son will be next year" __ 3(x+1)
"his wife is 20 years older than her son is this year" __ x+20
"there (sp) combined ages total 71" __ x+3(x+1)+x+20=71 __ 5x+23=71 __ x=9.6
age problems should have integer (whole number) solutions
__ when someone asks your age; it is 43, not 43 and 87 days
based on this; the son could be the same age next year, or 2 years older
__ depending on on the date relative to his birthday
the 2 year scenario is the only one leading to an integer solution
__ son is 9, John is 33, wife is 29
in retrospect, since an integer solution does exist; perhaps the author wanted us to think about the vagaries of ages
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! john is 3 times the age his son will be next year. his wife is 20 years older than her son is this year. there combined ages total 71. how old is each person.
:
Let their present ages be j, s, w
:
"john is 3 times the age his son will be next year."
j = 3(s+1)
:
"his wife is 20 years older than her son is this year."
w = (s + 20)
:
"there combined ages total 71" (I think they mean the combined ages of John and his wife only)
j + w = 71
:
how old is each person.
:
substitute for j and w:
3(s+1) + (s+20) = 71
:
3s + 3 + s + 20 = 71
:
4s + 23 = 71
:
4s = 71 - 23
s = 
s = 12
:
j = 3(13) = 39
w = 12+20 = 32
---------------
total age = 71
:
A rather ambiguous problem
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