Question

a two digit number is 4 times the sum of the digits it is also equal to 3 times the product of digits find the number

Answer 1

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)