Question 1103461: In 3 years, David will be 3 times as old as his sister martha. A year ago, david was 7 times older than martha. How old are they now?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
The problem is invalid. If the problem is worked with the information exactly as it is given, the ages turn out not to be whole numbers. In age problems like this, the ages have to be whole numbers.
The problem with the statement of the problem is with the statement that "a year ago, David was 7 times older than Martha".
If David is 7 times older than Martha and Martha's age is x, then David's age is that x, plus 7 times x, or x+7x=8x. In other words, "7 times older than" means the same as "8 times as old as".
Unfortunately, in everyday language "7 times older than" is incorrectly taken to mean the same as "7 times as old as". But incorrect grammar is not valid in the statement of a math problem in which a correct solution is to be obtained.
The fact that the two phrases are often used to mean the same thing is demonstrated by the complete statement of the problem, in which the phrases "3 times as old as" and "7 times older than" are both used -- apparently to be interpreted the same way.
If this is a problem from a teacher, tell him the statement of the problem is invalid.
If it is from a textbook, have your teacher write to the publisher to tell them that the statement of the problem is invalid.
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Addendum to my solution...
The link provided by tutor ikleyn (thank you...) shows the problem stated correctly, along with a correct solution.
Answer by ikleyn(52890)  (Show Source):
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