Results 1 to 4 of 4

Thread: Help me on digit problem T_T

  1. #1
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381

    Help me on digit problem T_T

    1.) The sum of the digits of a three - digit number is 17. The hundreds digit is thrice the tens digit. This number is 297 less than the number formed by reversing the order of the digits. What are the two numbers?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Aug 2006
    From
    Australia
    Posts
    12
    If the hundreds digit is twice the tens digit then the hundreds digit must be even.

    The hundreds digit then can't be less than 6 because half of 4 is 2 and 2+4=6 which then wouldn't enable a third number to add up to 17.

    Using 6 as the hundreds digit:

    Therefore the tens digit must be three and the last 8.

    The reverse then is 836, 836-638=198, so this is not the number.

    Using 8:
    The tens digit is 4
    And the last digit must be 5

    The reverse then is 548,

    845-548=297

    Numbers are 845 and 548.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    848
    Hello, ^_^Engineer_Adam^_^!

    [Random333, you missed the word "thrice".]

    1.) The sum of the digits of a three - digit number is 17.
    The hundreds digit is thrice the tens digit.
    This number is 297 less than the number formed by reversing the order of the digits.
    What are the two numbers?

    Since this is obviously an Algebra problem, I used an algebraic approach.

    Let H = hundreds digit, T = tens digit, U = units digit.

    Then the number is: . N \:=\:100H + 10T + U


    The sum of the digits is 17: . H + T + U\:=\:17 (1)

    The hundreds digit is three times the tens digit: . H\:=\:3T\quad\Rightarrow\quad H - 3T\:=\:0 (2)

    N is 297 less than its reversal . . . Its reversal is: . 100U + 10T + H
    Hence: . 100U + 10T + H) -" alt="100H + 10T + U \:=\100U + 10T + H) -" />  297\quad\Rightarrow\quad H - U \:=\:-3 (3)


    We have a system of equations: . \begin{array}{ccc}(1)\\(2)\\(4)\end{array} \begin{array}{ccc} H + T + U  \:= \:17 \\ H - 3T\qquad \:= \:0 \\ H\qquad - U \:= \:\text{-}3\end{array}

    . .Add (1) and (3): . . 2H + T \:=\:14
    Subtract twice (2): . -2H + 6T\:=\:0

    And we get: . 7T = 14\quad\Rightarrow\quad T = 2

    Substitute into (2): . H - 3(2)\:=\:0\quad\Rightarrow\quad H = 6

    Substitute into (1): . 6 + 2 + U \:=\:17\quad\Rightarrow\quad U = 9


    Therefore: . \boxed{N\:=\:629}, and its reversal is 926.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Jul 2006
    From
    Shabu City
    Posts
    381
    Thanks you sir!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Digit sum & digit product of number x
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Jan 19th 2011, 09:07 AM
  2. digit integer problem
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Oct 14th 2009, 01:00 PM
  3. Reverse Digit problem help
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Aug 18th 2009, 04:48 PM
  4. Four digit number problem?
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: Aug 18th 2009, 03:54 AM
  5. decimal digit as final digit
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Feb 25th 2008, 08:18 PM

Search tags for this page

the 3-digit number wherein the ones digit is three times the tens digit and the tens digit is three times the hundreds digit
,

The difference between a three digit number and number formed reversing the digits is 297

,

The difference between a three-digit number and the number formed by reversing the digits is 297. The sum of the units and tens digit is the same as the difference of the hundreds and the units digits. Also, the hundreds digit is twice the units digit. Fi

,

Q) the diff. btwn 3 dgt no. & the no. formed by reversing its digit is 297. The sum of the units digit and tens digit is the same as the difference of the 100s & the unit digits. Also , the 100s digit is twice the unit digit. Find the no.

,

a three digit number is equal to 19 times the sum of its digit.The tens digit is one more than the sum of the hundreds and units digits.If the digits are reversed the resulting number exceeds the original by 297.Find the no.?

,

A number formed by three digit if hundred digit is four times the unit digit if the sum digit is 14

,

on reversingthe order of digitand subtracting it from original number we get 297

,

A three digit number is such that twice the hundreds digit is more than the tens digit by 2.The unit digit is is thrice the hundreds digit.when the digits are reversed the number is increased by 594.Find the number.

,

has a hundred digit equal to the sum of the units and tens digits

,

the difference between a three- digit no.and no.fromed by reversing the digits is 297

,

difrence between a 3 digit no and the no formed by reversing digits is 396.the diffrence of hundreds and unit digit is 1 less thn sum of unut and tens digit also.also hundred digit is twice unut digit.finfd number

,

the difference between a three digit number and the number formed by reversing its digit is 297. the sum of the units and the tens digits is the same as the difference of the hundreds and the unit digits . also the hundreds digit is twice the units digit

,

the difference between a three digit number and the number formed by reversing its digit is 297. the sum of the units and the tens digits is the same as the difference of the hundreds and the unit digits . also the hundreds digit is twice the units digit

,

the difference between a three digit no and the no formed by reversing its digit is 297. the sum of the unit and tens digit is the same as the difference of the hundreds and the unit digits . Also, the hundreds digit is twice the units digit. Find the no?

,

in a two digit number the sum of the digit is 14. Twice the tens digit exeeds the unit digit by one.Find the numbers

Click on a term to search for related topics.

Search Tags


/mathhelpforum @mathhelpforum