SOLUTION: A father is 3 times older than his son. Both their ages add up to 54. What are their ages?

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Question 1180714: A father is 3 times older than his son.
Both their ages add up to 54.
What are their ages?
Found 3 solutions by MathLover1, greenestamps, josgarithmetic:
Answer by MathLover1(20849)   (Show Source):
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let father's age be and son's age
if a father is times older than his son, we have
....eq.1

if both their ages add up to , we have
....eq.2
substitute from eq.1

or and

then => or and

their ages are:
father is and years old
son is and years old

Answer by greenestamps(13200)   (Show Source):
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The statement of the problem is faulty. Age problems should have whole number answers; this one does not.

There is also a problem with the statement that the father is "3 times older than" his son. That is a phrase that is almost always used incorrectly to mean that if the son's age is x then the father's age is 3x.

But "3 times older than his son" means the son's age, x, PLUS "3 times more" his son's age (3x), making "3 times older than x" equal to x+3x=4x.

Note that is similar to an increase of 300% in a number making the number 4 times as big as it was previously. The original 100% of the number, plus the increase of 300%, makes a total that is 400% of the original number.

The statement of a math problem should NEVER use the phrase " 3 times older than" or "5 times larger than", because the intended meaning is almost never the correct meaning.

This problem is especially badly created, in that the solutions are not whole numbers with EITHER interpretation of the given information....

Answer by josgarithmetic(39617)   (Show Source):
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s, the son
3s+s, the father, or 4s

-------both ages sum to 54.

Son is years and Father is years of age.
Maybe recheck your problem description.