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Math Help - 2 hard word problems

  1. #1
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    2 hard word problems

    This is for a maths challenge thing I'm doing but I'm gonna change the numbers around a bit so that I'm not relying on others for help entirely. Please be really clear on the method and steps used- I know you guys are of great help but sometimes your understanding of maths just goes beyond my capabilties.

    1. Person A needs a $30. ATMs dispenses either $30, $40 or $70 notes. What is the largest amount he can withdraw to be certain that he has at least one $30 note?

    2. A certain positive integer X greater than 100 is displayed. But when its two rightmost digits are erased, the number left is X/154. Find all possible numbers of X.
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  2. #2
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    Hello, delicate_tears!

    Maybe I'm reading it wrong, but I don't understand #1 . . .


    2. A certain positive integer X greater than 100 is displayed.
    But when its two rightmost digits are erased, the number left is \frac{X}{154}.
    Find all possible values of X.

    We have the number: . X \;=\;"abc" \;=\;100a + 10b + c
    . . where b\text{ and }c are digits . . . and a is any positive integer.

    If the two rightmost digits are erased, the number becomes: . a
    . . which equals \frac{X}{154}

    So we have: . a \;=\;\frac{100a + 10b + c}{154} \quad\Rightarrow\quad 54a \:=\:10b + c

    Since 10b + c is a two-digit number, the only solution is: . a = 1,\:b = 5,\:c = 4


    Therefore: . X \;=\;154

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  3. #3
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    Hi Delicate_Tears,
    I can only imagine the solution to be $870. The Least Common Multiple of 30, 40, and 70 is $840. An ATM dispenser machine may give you $840 in bills of 30s only, 40s only, 70s only, or a mix between them. The only way to make sure that the bill has to give you a 30 dollar bill is to add 30 to the LCM.
    Last edited by Chop Suey; June 30th 2008 at 11:15 AM.
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