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Math Help - two-digit number

  1. #1
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    two-digit number

    please check:

    The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number? my answer is 94?
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  2. #2
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    Quote Originally Posted by ronaldj View Post
    please check:

    The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number? my answer is 94?
    Let x be the original two-digit number. Then, the new number is:

    10x + 3. Now, we know that 10x + 3 = x + 372

    Solving this gives us:

    9x = 369 \Rightarrow x = 41

    How did you arrive at 94? You should have easily noted that if you modify the number as stated you get 943, which is obviously not 372 more than 94.
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  3. #3
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    Quote Originally Posted by ronaldj View Post
    please check:

    The digit 3 is written at the right of a certain two-digit number thus forming a three-digit number. The new number is 372 more than the original two-digit number. What was the original two-digit number? my answer is 94?
    Let the original number be 10x +y with x\in\{1, 2, ..., 9\} and y\in\{0, 1, 2, ..., 9\}

    Then the 3-digit-number is 100x+10y+3.

    According to the wording of the question you get:

    100x+10y+3-372=10x+y

    10x+y=41

    The only possible value for x = 4 and y = 1. Thus the original number is 41.
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  4. #4
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    Quote Originally Posted by Defunkt View Post
    Let x be the original two-digit number. Then, the new number is:

    10x + 3. Now, we know that 10x + 3 = x + 372

    Solving this gives us:

    9x = 369 \Rightarrow x = 41

    How did you arrive at 94? You should have easily noted that if you modify the number as stated you get 943, which is obviously not 372 more than 94.
    Mea culpa. You are right - thanks!
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  5. #5
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    Quote Originally Posted by earboth View Post
    Let the original number be 10x +y with x\in\{1, 2, ..., 9\} and y\in\{0, 1, 2, ..., 9\}

    Then the 3-digit-number is 100x+10y+3.

    According to the wording of the question you get:

    100x+10y+3-372=10x+y

    10x+y=41

    The only possible value for x = 4 and y = 1. Thus the original number is 41.
    QUESTION - my kid wants to know if it could also be 21 since 21 + 372 = 393/
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  6. #6
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    Quote Originally Posted by ronaldj View Post
    QUESTION - my kid wants to know if it could also be 21 since 21 + 372 = 393/
    If you add 3 to the right of 21, do you get 393?
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  7. #7
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    you are sooh right!

    My head hurts but you are right.

    Tx for pointing out our mistake!
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