SOLUTION: wht is the solution of, a two digit number is four times the sum of its digits and thrice the product of its digits. find the number.

t = tens digit
u = ones digit
the two digit number = 10t+u
t+u = sum of the digits
tu = product of the digits

So 



Distribute on the right



Simplify:



Divide both sides by 3

So we have this system of equations:



Substitute  for  in the 2nd equation





Combine terms on the left



Divide through by 6







Factor out 



Set each factor = 0

   
             

The ten's digit cannot be 0 for a 2-digit number.

So  

Substitute that in 







So since  and ,

The number is .

Checking:

The sum of the digits is 2+4 or 6

So 24 is 4 times the sum of its digits, 
because 24 is 4 times 6.

The product of the digits is 2×4 = 8

So 24 is thrice the product of its digits,
because 24 is 3 times 8.

It checks.  

Edwin