From: Lynn Killingbeck Subject: Re: an age question Date: Sat, 11 Sep 1999 02:39:47 -0500 Newsgroups: sci.math Keywords: one way to approach word problems (regula falsi) TNT1120 wrote: > > A woman was asked how old her children were: > > She answered, "Mary is 24 years old and John doesn't like to tell his age, but > Mary is twice as old as John was when Mary was as old as John is now. " > > What is John's age? Found what may be the original version, on some badly yellowed paper. I wonder who originated this! Hope I didn't botch the transcription. --------------------------------------------- The sum of Mary's and Ann's ages is 44 years. Mary is twice as old as Ann was when Mary was half as old as Ann will be when Ann is three times as old as Mary was when Mary was three times as old as Ann. How old is Mary? --------------------------------------------- Lynn Killingbeck ============================================================================== From: "William L. Bahn" Subject: Re: an age question Date: Sat, 11 Sep 1999 04:05:58 -0600 Newsgroups: sci.math Lynn Killingbeck wrote in message <37DA0743.218D@phoenix.net>... [see above --djr] This IS an interesting problem. I see a couple ways of tackling it, but since MAppell917 gave me such grief for the suggestion I gave TNT1120, I will use that technique to figure out how to approach this problem. This was my suggestion when TNT1120 asked how old John was: To quote myself: 42. And if you don't believe me, test it. If you test it and find that it isn't true, then take a careful look at how you tested it and what number would have passed your test. To misuse a cliche, let's put my money where my mouth is: Assume that Mary is 30 years old. How do I test that assumption? Simple, walk through the problem. (1) If Mary is 30 years old that makes Ann 14 years old which means that Mary is 16 years older than Ann. (2) When Mary was three times older than Ann, Ann was 8 years old and Mary was 24 years old. (3) When Ann is three times older than Mary was then, she will be 72 years old. (4) When Mary was half that age she was 36 years old and Ann was 20 years old. (5) If Mary is currently twice as old as Ann was then, she must be 40 years old - which is NOT the answer we assumed so that answer must be wrong. But let's look carefully at how I tested the assumed answer. The key appears to be the age differential, most of the calculations seemed to build off of half of that value. So, if Mary is 2X years older than Ann, that means the following: (2) When Mary was three times older than Ann, Ann was X years old and Mary was 3X years old. (3) When Ann is three times older than Mary was then, she will be 9X years old. (4) When Mary was half that age she was 4.5X years old and Ann was 2.5X years old. (5) If Mary is currently twice as old as Ann was then, she must be 5X years old now and Ann must be 3X years old. We know that 5X + 3X = 44 which makes X=5.5 (And I'm not abusing units - X is unitless because, for readability, I left the units explicit and external to X). That means that Mary is now 27.5 years old. To quote MAppell917: Do you think a "test it and see" will get him any further? What's the point of having a newsgroup if everyone gives wrong answers with a response of "test it and see." What help is that? You tell me? I offered a powerful and general problem solving technique - you simply worked a particular problem for him. Which will get him further?