# Thread: What is the number?

1. ## 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?

2. Originally Posted by Ellla
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.

3. 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

4. Thank you. I got it right now

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