Question 1191544: John is X years old
Jill is 2 years younger than John
Tom (John's dad) is 2x older than John plus 8 years
How old is John, Jill and Tom
Total ages added together is 82
Found 3 solutions by ankor@dixie-net.com, greenestamps, josgarithmetic:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! John is X years old
Jill is 2 years younger than John
(x-2) = Jill's age
Tom (John's dad) is 2x older than John plus 8 years
(2x+8) = Dad's age
How old is John, Jill and Tom
Total ages added together is 82
x + (x-2) +(2x+8) = 82
x + x + 2x - 2 + 8 = 82
4x + 6 = 82
4x = 82-6
4x = 76
x = 76/4
x = 19 is John's age
19 - 2 = 17 is Jill's
2(19)+8 = 46 is Dad's
:
Check: 19 + 17 + 46 = 82
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Technically, the problem as stated has no solution in whole numbers and is therefore invalid.
The problem is that a phrase like "2 times older than" should NEVER be used in the statement of a problem, because its meaning is NOT what most people think it is.
Given an age n, the age "2 times AS OLD AS" n is clearly 2*n = 2n. That is clearly what the intent of this problem is.
But if an age n is given, and another age is "2 times OLDER THAN" n, then the grammatically correct interpretation is that the other age is n, PLUS 2 TIMES MORE n, which is n+2n=3n.
(Note that corresponds to saying that a number INCREASED BY 200%, becomes 100%+200% = 300% of the original number.)
So "2 times older than" means "3 times as old as".
Then the correct interpretation of the problem as written is
x = John's age
x-2 = Jill's age
3x+8 = Tom's age
And the equation that says the sum of their ages is 82 leads to non-integer values:
x+(x-2)+(3x+8)=82
5x+6=82
5x=76
x=15.2
Answer by josgarithmetic(39617)  (Show Source):
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