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Math Help - Money Math-Trick Question

  1. #1
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    Money Math-Trick Question

    Kane has $50.00. He goes to the supermarket and buys football boots and then he buys a soccer ball, which is half the price of the football boots.He then spends half of what she has left on a belt, leaving him with $15.00.

    How much did the soccer ball cost?

    How much did the football boots cost?

    I started it like this:

    Let x= price of football boots

    Let 1/2(x) = price of soccer ball

    the combined cost of soccer ball and football boots = x + 1/2(x)

    Amount spent on the football boots and soccer ball :

    $50-(

    I am stuck

    The text gives a clue that the price of the belt = $15
    (How did they arrive at the conclusion that the price of the belt equals $15?)

    Anyone has any ideas as to how I can move on?

    Thanks
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  2. #2
    Member anonimnystefy's Avatar
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    Re: Money Math-Trick Question

    let y be the amount of money after he buys both football and soccer boots.then the price of the belt is 1/y.after buying the belt he has $15.so the equation is:
    y-y/2=$15

    can you solve it from here?
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Money Math-Trick Question

    Quote Originally Posted by KayPee View Post
    Kane has $50.00. He goes to the supermarket and buys football boots and then he buys a soccer ball, which is half the price of the football boots.He then spends half of what she has left on a belt, leaving him with $15.00.

    How much did the soccer ball cost?

    How much did the football boots cost?

    I started it like this:

    Let x= price of football boots

    Let 1/2(x) = price of soccer ball

    the combined cost of soccer ball and football boots = x + 1/2(x)

    Amount spent on the football boots and soccer ball :

    $50-(

    I am stuck

    The text gives a clue that the price of the belt = $15
    (How did they arrive at the conclusion that the price of the belt equals $15?)

    Anyone has any ideas as to how I can move on?

    Thanks
    Let x be the price of the boots

    After buying the football and the football boots he is left with: y = \left[50 - \left(x+ \dfrac{x}{2}\right)\right]

    He then spends half of this on the belt and is left with $15:  y - \dfrac{y}{2} = 15

    Of course we have an expression for y in x so sub that in:

    \left[50 - \left(x+ \dfrac{x}{2}\right)\right] - \dfrac{1}{2}\left[50 - \left(x+ \dfrac{x}{2}\right)\right] = 15

    And after simplification:

    \left(50 - \dfrac{3x}{2}\right) - \left(25 - \dfrac{3x}{4}\right) = 15

    Solve for x, which is the price of the boots
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  4. #4
    MHF Contributor

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    Re: Money Math-Trick Question

    Quote Originally Posted by KayPee View Post
    Kane has $50.00. He goes to the supermarket and buys football boots and then he buys a soccer ball, which is half the price of the football boots.He then spends half of what she has left on a belt, leaving him with $15.00.
    Well, you said this was a trick question! Who is "she" and how much money does she have?

    How much did the soccer ball cost?

    How much did the football boots cost?

    I started it like this:

    Let x= price of football boots

    Let 1/2(x) = price of soccer ball

    the combined cost of soccer ball and football boots = x + 1/2(x)

    Amount spent on the football boots and soccer ball :

    $50-(

    I am stuck

    The text gives a clue that the price of the belt = $15
    (How did they arrive at the conclusion that the price of the belt equals $15?)

    Anyone has any ideas as to how I can move on?

    Thanks
    You were told that he spent "half of what [s]he has left on a belt" and then had $15 left. If you spend "half", you have "half" left.

    That means that before buying the belt, he had $30. That means that the boots and ball cost 50- 30= $20. Taking x to be the cost of the boots, the ball cost x/2 so x+ x/2= 3x/2= 20.
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