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Math Help - Stupidly simple, yet confusing (For me) sales problem

  1. #1
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    Stupidly simple, yet confusing (For me) sales problem

    What is the difference, please explain..!!

    A pair of shoes is normally priced at $37. What will be the sale price if a 25% sales discount is offered?

    I would assume i reduce $37 by 25%, i.e 37/1.25 = $29.60
    However the answer is $37 x 0.75 = $27.75.

    What is the difference in arising to the two unique solutions?
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  2. #2
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    Re: Stupidly simple, yet confusing (For me) sales problem

    To reduce a quantity A by 25%, you need to take 100% of A minus 25%.

     (1-0.25)A = 0.75A

    By dividing by 125%, you're really reducing the quantity by 20%.

     \frac{1}{1.25}A = 0.8A = (1 - 0.20)A
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  3. #3
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    Re: Stupidly simple, yet confusing (For me) sales problem

    Quote Originally Posted by audusdyengbp View Post
    I would assume i reduce $37 by 25%, i.e 37/1.25 = $29.60
    That's a very neat way of reversing a 25% increase.

    You probably learnt it long ago in a lesson that was all about the difference you're asking about here, i.e. the very big difference between reducing by 25% and reversing a 25% increase.

    Funny thing is, reversing should be the trickier of the two, but you've 'over-learnt' it, and are applying it regardless, just like most people (before that lesson) try to reverse a 25% increase by reducing by 25%.

    So you need to get back in touch with the more obvious intuition. I suggest the following.

    Think of the $37 as a tower of 4 bricks. You've been asked to remove the top one.

    What you tried was a way of removing a fifth brick placed on the top.
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    Re: Stupidly simple, yet confusing (For me) sales problem

    Quote Originally Posted by JohnDMalcolm View Post
    To reduce a quantity A by 25%, you need to take 100% of A minus 25%.

     (1-0.25)A = 0.75A

    By dividing by 125%, you're really reducing the quantity by 20%.

     \frac{1}{1.25}A = 0.8A = (1 - 0.20)A
    now this makes sense.

    the reason i did 37/1.25 to reduce by 25% is due to my financial instruments class where we have to discount a bond value back to its present value.
    i.e if the future value of a bond 1 year from now is $1000, and interest rates are currently 5% then the present value is the future value DISCOUNTED back to one period at the interest rate, being 1000/1.05.

    thank you.

    if anyone can offer any more clarification, it would be appreciated.
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  5. #5
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    Re: Stupidly simple, yet confusing (For me) sales problem

    Quote Originally Posted by tom@ballooncalculus View Post
    That's a very neat way of reversing a 25% increase.


    You probably learnt it long ago in a lesson that was all about the difference you're asking about here, i.e. the very big difference between reducing by 25% and reversing a 25% increase.


    Funny thing is, reversing should be the trickier of the two, but you've 'over-learnt' it, and are applying it regardless, just like most people (before that lesson) try to reverse a 25% increase by reducing by 25%.


    So you need to get back in touch with the more obvious intuition. I suggest the following.


    Think of the $37 as a tower of 4 bricks. You've been asked to remove the top one.


    What you tried was a way of removing a fifth brick placed on the top.


    actually im still confused.

    lets look at it this way:

    increasing $1000 by 25% is 1000 x 1.25 = $1250
    now if we reduce $1250 by 25% again, are you saying it is $1250 x 0.75 = $937.50, and not $1250/1.25 = $1000?

    Because $1250/1.25 is an 20% reduction (1/1.25 = 0.8).

    this is correct?


    EDIT:

    so lets say i do add that 5th brick, then if i take 25% of the 5 brick structure, i get ((37 x 0.75 = 27.75).
    Using this brick logic, how would you interpret 37/1.25 = 29.6 then?
    Last edited by audusdyengbp; August 7th 2012 at 06:44 PM.
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  6. #6
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    Re: Stupidly simple, yet confusing (For me) sales problem

    Quote Originally Posted by audusdyengbp View Post
    actually im still confused.

    lets look at it this way:

    increasing $1000 by 25% is 1000 x 1.25 = $1250
    now if we reduce $1250 by 25% again, are you saying it is $1250 x 0.75 = $937.50, and not $1250/1.25 = $1000?

    Because $1250/1.25 is an 20% reduction (1/1.25 = 0.8).

    this is correct?
    Yes! Totally.

    Quote Originally Posted by audusdyengbp View Post
    EDIT:

    so lets say i do add that 5th brick, then if i take 25% of the 5 brick structure, i get ((37 x 0.75 = 27.75).
    Although you can't do this without sawing into one of the bricks. Embarking on a 25% reduction in the first place should tell you to look at the given amount as a tower of 4 not 5.

    Quote Originally Posted by audusdyengbp View Post
    Using this brick logic, how would you interpret 37/1.25 = 29.6 then?
    As removing one of 5 bricks.

    Or as reducing by 20%.

    Or as dividing by five quarters (which would reverse a multiplication by five quarters which is an increase by one quarter).
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  7. #7
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    Re: Stupidly simple, yet confusing (For me) sales problem

    Quote Originally Posted by tom@ballooncalculus View Post
    Yes! Totally.



    Although you can't do this without sawing into one of the bricks. Embarking on a 25% reduction in the first place should tell you to look at the given amount as a tower of 4 not 5.



    As removing one of 5 bricks.

    Or as reducing by 20%.

    Or as dividing by five quarters (which would reverse a multiplication by five quarters which is an increase by one quarter).
    Tom, Mate - you are a legend!

    Thanks
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