SOLUTION: Jack is two years younger than Jill which is 3 times John’s age. If the sum of their ages is 23. How old is Jill?

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Question 1163555: Jack is two years younger than Jill which is 3 times John’s age. If the sum of their ages is 23. How old is Jill?
Found 4 solutions by josgarithmetic, ikleyn, solver91311, greenestamps:
Answer by josgarithmetic(39630)   (Show Source):
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PERSON AGE Jack 3n-2 Jill 3n John n SUM 23

Answer by ikleyn(52903)   (Show Source):
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Jack is two years younger than Jill which is 3 times John’s age. If the sum of their ages is 23. How old is Jill?
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Let John age be x years. Then Jill's age is 3x years. Then Jack's age is (3x-2) years. The sum of ages equation is x + 3x + (3x-2) = 23 It implies 7x = 23 + 2 = 25.

As worded, printed, posted and presented, this problem HAS NO solution in integer numbers.

Good only for re-cycling.

Where, from which garbage box did you recover it ?

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"Paraphrase" in the post by @greenestamps is NOT EQUIVALENT to the original formulation --- hence,

it is not a paraphrase, at all. It is different formulation, so his solution is irrelevant to the given post.

It relates to another/different problem.

Answer by solver91311(24713)   (Show Source):
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Your problem is ambiguously worded. If you interpret the problem as Jill's age being 3 times John's age, you get a non-integer solution. However, if you interpret the problem to mean Jack's age is 3 times John's age, it works:

Let represent Jill's age, then represents Jack's age, and represents John's age.

Solve for and you should discover that Jill is 11, making Jack 9 and John 3 for a total of 23 as requested.

John

My calculator said it, I believe it, that settles it

Answer by greenestamps(13214)   (Show Source):
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I don't read any ambiguity into the statement of the problem. It is, however, poorly worded. Paraphrased, it says this:

"Jack's age, which is two years less than Jill's age, is 3 times John's age."

And from there I would use John's age as my variable, to avoid working with fractions -- which is nearly always easier.

x = John's age
3x = Jack's age
3x+2 = Jill's age

The sum of their ages is 23:

ANSWER: their ages are
John: x = 3
Jack: 3x = 9
Jill: 3x+2 = 11