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Maths quiz problem help, please year 9 top set

Discussion in 'Mathematics' started by stella66, Mar 29, 2007.

  1. Mr Kitto was exactly 5 years older than his wife and they had two children, who were twins and went to the local comprehensive school.
    One evening, one of the twins (who had just been given a calculator) announced that if you multiplied together the parents' ages, and then added together the twins' ages, and divided one result by another, the answer was 57 exactly.
    How old was Mr Kitto?
     
  2. Mr Kitto was exactly 5 years older than his wife and they had two children, who were twins and went to the local comprehensive school.
    One evening, one of the twins (who had just been given a calculator) announced that if you multiplied together the parents' ages, and then added together the twins' ages, and divided one result by another, the answer was 57 exactly.
    How old was Mr Kitto?
     
  3. bombaysapphire

    bombaysapphire Star commenter

    He's 38, his wife is 33 and the twins are both 11. I used the quadratic formula and a spreadsheet to find a whole number answer.
     
  4. Thanks Bombay,can you give the quadratic equation you formed please?
     
  5. bombaysapphire

    bombaysapphire Star commenter

    I called Mr K's age k and the twins age t.

    k(k-5)/2t = 57
    k^2 - 5k = 114t
    k^2 - 5k - 114t = 0

    Using the formula I needed to find 25 + 456t to give a square number for a whole number answer. The only solution in the range t= 11 to 17 was t=11.

     
  6. Great, thank you!
     
  7. Re: Post 4

    k(k-5)/2t=57 assumes the children are younger than the parents.

    What about if the twins are older than their parents?

    2t/k(k-5)=57


    hmm
     
  8. bbibbler

    bbibbler New commenter

    Now I know why I have missed this place so much

    Re whole number answers, is age descete or continuous?
     
  9. Andrew Jeffrey

    Andrew Jeffrey New commenter

    There is an interesting point here about how much of our experience we bring to bear on a problem, and how much our different viewpoints will cause us to approach things in different ways.For example, I have been guilty in the past of using an algebraic sledgehammer to crack a very small nut, when a bit of common sense would have got me there quicker.
    SAM: If you give me one of your sweets I will have twice as many as you,"
    JO: "If you give me one of your sweets, we will have the same number." How many did each have?
    I went straight into simultaneous equations, when I could probably have solved it much faster - the difference must be 2, giving one away would make the difference 4 etc...
     
  10. Andrew Jeffrey

    Andrew Jeffrey New commenter

    There is an interesting point here about how much of our experience we bring to bear on a problem, and how much our different viewpoints will cause us to approach things in different ways.For example, I have been guilty in the past of using an algebraic sledgehammer to crack a very small nut, when a bit of common sense would have got me there quicker.
    A quick ancedotal case - this evening I was preparing a talk on Primary problem solving. I came across the following simple problem:
    SAM: If you give me one of your sweets I will have twice as many as you,"
    JO: "If you give me one of your sweets, we will have the same number." How many did each have?
    I went straight into simultaneous equations, when I could probably have solved it much faster - the difference must be 2, giving one away would make the difference 4 etc...
     
  11. Andrew Jeffrey

    Andrew Jeffrey New commenter

    Sorry - I missed a tag the first time around and it didn't make sense...not that it made much more sense at the second attempt!
     
  12. See also http://thesciencepundit.blogspot.com/2006/07/john-von-neumann-and-mathematicians.html
     
  13. DeborahCarol

    DeborahCarol New commenter

    This could also be done by 'systematic' trial and error, as follows.
    The twins' ages could be anything between 11 and 18. Not too many possibilities there, so let's start at 11.
    (Mum's age x Dad's age) / 2 x twins' ages = 57
    If the twins are 11, that would make Mum's age x Dad's age: (57 x 22) = 1254
    Now look for whole-number factor pairs for 1254.
    I started at 27 (unlikely that one of the parents in a school quiz maths question would be younger than this!) and the first whole number factor pair I found was 33 and 38. Test: yes, they're five years apart. Done!
    After puzzling over this one, grateful for others for pointing out it didn't have to be done with quadratics, as the top set Year 9 student I know wouldn't have been able to do it that way. I wanted to find another way of doing it, and I had no joy late last night. :) This morning - no problem.
    I do feel the wording of the question could be improved, ie change 'divided one result by another' to 'divide the first result by the second'.
     
  14. I read an example of this in "Incognito" by David Eagleman. It goes something like this: There are four cards, each with a shape on one side and a number on the other. You can see a square, a triangle, 46 and 15.
    Which two cards do you have to turn over to test the rule: " Any card with a square has an even number on the other side"?


    When the problem is posed differently, the problem becomes easier (as proved by some experiments): The cards have the age of a person and what they are drinking. You can see whisky, lemonade, 46 and 15.
    Which two cards do you need to turn over to test the rule "Only adults should drink alcohol"?

    Less than a quarter of people answer the first problem correctly, whereas more than half answer the second correctly.
     
  15. That's really interesting ... I found the first wording so much easier. I had to re-read the second one a few times to get the meaning (even thought you had pointed out that it was basically the same thing, just with different wording).
    I think it also highlights the habit of people (all ages, not just pupils) thinking "oh, maths! no chance, I can't do that". Defences go up, confidence goes down and they end up being right ... they can't do it. Say to yourself "I can do that", and the defences go down, confidence goes up and they end up being right again ... they can do it.
     

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