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Math Help - Notebook Cost

  1. #1
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    Notebook Cost

    John and his twin brothers each bought three identical notebooks when school started in August. John paid for the notebooks with a $10 bill. He received less than $0.50 in change, all in nickels. No sales tax was charged. What was the price paid for one notebook?
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by aznmartinjai View Post
    John and his twin brothers each bought three identical notebooks when school started in August. John paid for the notebooks with a $10 bill. He received less than $0.50 in change, all in nickels. No sales tax was charged. What was the price paid for one notebook?
    The total cost of all three notebooks was some amount of money less than $10 but greater than $9.50. So we need some amount between those two numbers that is divisible by 0.05 (since all the change was in nickles) AND is divisible by 3 (since this is the price for three books).

    If we divide $10 by 3, we get $3.333333... (repeats)
    If we divide $9.50 by 3, we get $3.1666666... (repeats)

    We could use trial and error to see what the amount is by testing numbers between 9.50 and 10.00 that are multiples of 0.05:

    $9.55/3 doesn't work
    $9.60/3 = $3.20
    $9.65/3 doesn't work
    $9.70/3 doesn't work
    $9.75/3 = $3.25
    $9.80/3 doesn't work
    $9.85/3 doesn't work
    $9.90/3 = $3.30
    $9.95/3 doesn't work

    There are three answers that work: $3.20, $3.25, $3.30. I'm not sure if I missed something in your explanation of the problem.
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  3. #3
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    3 answers? huh..? are you sure?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by aznmartinjai View Post
    John and his twin brothers each bought three identical notebooks when school started in August. John paid for the notebooks with a $10 bill. He received less than $0.50 in change, all in nickels. No sales tax was charged. What was the price paid for one notebook?
    ecMathGeek's logic is correct, however, the mistake was he was trying to account for three notebooks when he should have accounted for nine. Recall, John and his twin brothers each bought three identical notebooks. so that's John and two other boys, so that's 3 per boy which is 9 notebooks. so following ecMathGeek's logic of trial and error, we find:

    $9.55/9 doesn't work
    $9.60/9 = doesn't work
    $9.65/9 doesn't work
    $9.70/9 doesn't work
    $9.75/9 = doesn't work
    $9.80/9 doesn't work
    $9.85/9 doesn't work
    $9.90/9 = $1.10 each notebook
    $9.95/9 doesn't work
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  5. #5
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by Jhevon View Post
    ecMathGeek's logic is correct, however, the mistake was he was trying to account for three notebooks when he should have accounted for nine. Recall, John and his twin brothers each bought three identical notebooks. so that's John and two other boys, so that's 3 per boy which is 9 notebooks. so following ecMathGeek's logic of trial and error, we find:

    $9.55/9 doesn't work
    $9.60/9 = doesn't work
    $9.65/9 doesn't work
    $9.70/9 doesn't work
    $9.75/9 = doesn't work
    $9.80/9 doesn't work
    $9.85/9 doesn't work
    $9.90/9 = $1.10 each notebook
    $9.95/9 doesn't work
    Ha! I didn't see that.

    Good job, Jhevon.
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ecMathGeek View Post
    Ha! I didn't see that.

    Good job, Jhevon.
    Aw, shucks, let's just call it luck
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  7. #7
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    Would that be "Lucky Number Jhevon"?

    Quote Originally Posted by Jhevon View Post
    Aw, shucks, let's just call it luck
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