Question

a two digit number is four times the sum of the digits.it is also equal to 3 times the product of digits .find the number​

Answer 1

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>> two digits, x & y

10x + y = the number

:

>> A two digit number is 4 times the sum of its digits

10x + y = 4(x+y)

10x + y = 4x + 4y

10x - 4x = 4y - y

6x = 3y

>> divide both sides by 3

2x = y

>> " and twice the product of its digit."

10x + y = 2xy

>> Replace y with 2x

10x + 2x = 2*x*2x

12x = 4x^2

>> Divide both sides by 4x

3 = x

then

y = 2(3)

y = 6

:

>> the number = 36

:

>> You can confirm this in both statement:

36 = 4(3+6)

and

36 = 2(3*6)

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Answer 2

Answer:

Step-by-step explanation:

A two digit positive integer can be expressed as 10x+y,

where xis the tens digit and y is the ones digit.

 

So, 10x+y = 4(x+y)  and 10x+y = 3xy

 

10x+y = 4x+4y

 

      6x = 3y

 

        y = 2x

 

Since y = 2x and 10x+y = 3xy, we have 10x+2x=3x(2x)

12x = 6x2

6x²-12x=0

6x(x-2) = 0

Since x≠0

x=2

y=2×2=4

Required number is 24.

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