Question 1183017: Mr John is 55years old. 15 years ago,he was 4 times older than his son.How old is his son now.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The language used in the statement of the problem makes it impossible to know what the right answer is.
The phrase "4 times older than" should NEVER be used in the statement of a math problem.
If one person's age is x, then the correct interpretation of "4 times OLDER THAN x" is x, plus 4 more times x, or x+4x=5x.
On the other hand, if one person's age is x, then "4 times AS OLD AS x" would clearly be just 4x.
Unfortunately, sloppy use of everyday language nearly always has the two different phrases meaning the same thing.
So when the phrase is used in the statement of a math problem, we have no way of knowing which interpretation is correct. (But very probably the intended interpretation is the grammatically incorrect one.)
(1) The grammatically incorrect solution....
Let x be the son's age 15 years ago
Then 4x is John's age 15 years ago
John is 55 now, so 15 years ago his age was 40.
That means 15 years ago his son was 40/4=10.
And that means the son's age now is 10+15 = 25.
(2) The grammatically correct solution...
Let x be the son's age 15 years ago
Then x+4x=5x is John's age 15 years ago
John is 55 now, so 15 years ago his age was 40.
That means 15 years ago his son was 40/5=8.
And that means the son's age now is 8+15 = 23.
Very often is is possible to tell which interpretation is the intended one, because one interpretation will give a whole number answer and the other will not. And if that is the case, then nearly always the one that gives a whole number answer is the grammatically INCORRECT one -- which means the author of the problem is using sloppy language.
But in this problem, we can't tell which is the intended interpretation, because both give whole number answers.
Answer by josgarithmetic(39620)  (Show Source):
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