SOLUTION: I'm four times older than my sister was when she was half as young as I was. In 15 years our combined age will be 100. How old are we now?

Question 1095314: I'm four times older than my sister was when she was half as young as I was. In 15 years our combined age will be 100. How old are we now?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

With the problem as shown, there is no solution.

The problem is with the phrase "... four times older than...". In sloppy everyday usage, that means the same as "four times AS OLD AS"; however, the correct grammatical interpretation of "four times older than x" means x, plus x 4 more times, for a total of 5x.

In virtually every problem I have seen where the phrase " x times greater than" is used, the problem only has a solution if the grammatically improper interpretation is used. That is, sadly, the case in your problem. The only way to get a solution to the problem is to interpret "four times older than" to mean the same as "four times as old as".

So, moving ahead with that interpretation, let x be your sister's age when she was half as old as you. Then your age then was 2x; and that means the difference between your ages is x.

The problem says you are 4 times as old as you sister was then; that makes your current age 4x. And since the difference between your ages is x, your sister's current age is 3x.

If your combined ages 15 years from now will be 100, then your current combined ages is 70. So...

Your current ages are
4x = 40
and
3x = 30
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