SOLUTION: Maricar is ten times older than her son Carl. In five years, the product of her age and son’s age two years ago will be 35. Find their present ages

Question 1171186: Maricar is ten times older than her son Carl. In five years, the product of her age and son’s age two years ago will be 35. Find their present ages
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
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Maricar is ten times as old as her son Carl.
In five years, the product of her age and son’s age two years ago will be 35. Find their present ages
~~~~~~~~~~~~~~~~

            Please pay attention how I edited your post
            to give it a RIGHT form, WHICH IT SHOULD HAVE.

35 = 1*35 = 5*7 = 7*5 = 35*1 Based on common sense, the only possible solution is THIS the son's age two years ago was 1 year; The mother's age in five years will be 35 years. Which implies that NOW they are 3 years old (the son) and 30 years old (the mother). ANSWER

Solved.

/\/\/\/\/\/\/\/

If you are going to be at this forum, then LEARN please how to use the form

            "ten times as old as the other person".

You use it INCORRECTLY in your post, and you will suffer all the time
until you learn the RIGHT FORM.

Learn English from my post in parallel with Math, and have doubled (or even TRIPLED) benefits (!) - for free . . .

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The statement of the problem is awkward and open to different interpretations; and the problem only has a solution if an invalid interpretation is used.

First look at the statement "In five years, the product of her age and son’s age two years ago will be 35."

The two ages in that statement are undoubtedly the mother's age 5 years from now and the son's age 2 years ago. But, because of the awkward phrasing, it could also be interpreted as the mother's age 5 years from now and the son's age 2 years BEFORE THAT, which would be 3 years from now.

The statement should read "The product of her age 5 years from now and her son's age two years ago is 35."

Given that interpretation, the only sensible answer is that the mother's age 5 years from now will be 35 and her son's age 2 years ago was 1; that makes her age now 30 and her son's age now 3.

But that answer is incompatible with the other given information, because the other information is given incorrectly.

Unfortunately, in everyday usage, "ten times as old as" and "ten times older than" are used to mean the same thing; but they do not.

"ten times AS OLD AS x" means 10 times x, or 10x.

"ten times OLDER THAN x" means x, plus 10 more times x, which is x+10x = 11x.

In the given problem, the answer that the mother is 30 and the son is 3 means that the mother is 10 times AS OLD AS her son. But the problem says she is 10 times OLDER THAN her son; and that is not true.

So the bottom line on this problem is that there is no solution the problem as given.

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