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Math Help - What is the number?

  1. #1
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    What is the number?

    Double-digit number is divided by its number total = quotient 4 and remainder 3. If we divide the same number by its figures product, we get a quotient 3 and remainder 5. What is that double-digit number?

    Sorry for my English, just trying my best. Double-digit number is, lets say, XY.

    XY / X+Y = quotient 4 and remainder 3. I think that means xy = 4(x+y) + 3.

    Now we have to divide(I guess?) the same number. If so, 4(x+y) + 3 / x*y = quotient 3 and remainder 5.

    I dunno, if I got it right ;\ Answer is: 23. But how do I get that? Can you help me?
    Last edited by Ellla; December 5th 2010 at 09:24 AM. Reason: Solved
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  2. #2
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    Quote Originally Posted by Ellla View Post
    Double-digit number is divided by its number total = quotient 4 and remainder 3. If we divide the same number by its figures product, we get a quotient 3 and remainder 5. What is that double-digit number?

    Sorry for my English, just trying my best. Double-digit number is, lets say, XY.

    XY / X+Y = quotient 4 and remainder 3. I think that means xy = 4(x+y) + 3.

    Now we have to divide(I guess?) the same number. If so, 4(x+y) + 3 / x*y = quotient 3 and remainder 5.

    I dunno, if I got it right ;\ Answer is: 23. But how do I get that? Can you help me?
    1. A two-digit-number with the digits x andy is written as 10x +y

    2. According to your considerations you have:

    10x + y = 4(x+y)+3

    10x+y=3xy+5

    3. Determine y from the 1st equation and replace y in the 2nd equation by this term:

    10x+(2x-1)=3(2x-1)\cdot x +5

    4. Solve for x.
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  3. #3
    MHF Contributor Unknown008's Avatar
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    No, you should say that the digits are X and Y and hence, the number becomes 10X + Y

    Hence, for the first statement, you get:

    \dfrac{10X + Y}{X + Y} = 4 and R = 3

    That is:

    \dfrac{10X + Y}{X + Y} = 4+  \dfrac{3}{X + Y}

    And the second statement:

    \dfrac{10X + Y}{XY} = 3 and R = 5

    and:

    \dfrac{10X + Y}{XY} = 3+  \dfrac{5}{XY}

    You have 2 equations and 2 unknowns, find X and Y.

    EDIT: Again, too late XD
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  4. #4
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    Thank you. I got it right now

    Oh, how could I have forgotten that xy is written as 10x + y...
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