Question 335162
the 2 digits are a and b


a is the tens digit and b is the units digit.


the value of the 2 digit number is given by the equation:


number = 10*a + b


the number is equal to 6 times the sum of the digits of the number.


this means that:


number = 6 * (a + b) which means that:


10a + b = 6 * (a + b)


Simplify this to get:


10a + b = 6a + 6b


subtract 6a from both sides of this equation to get:


4a + b = 6b


subtract b from both sides of this equation to get:


4a = 5b


divide both sides of this equation by 4 to get:


a = (5/4) * b


You can be any number where both a and b are integers.


That appears to happen when b is a multiple of 4.


when b = 4, a = 5.


when b = 8, a = 10.


when b = 12, a = 15.


etc.


Take any multiple of 4 for b, and you should be able to see that the equation comes true.


Assume b = 16


This make a = 5*16/4 = 5*4 = 20


You have a = 20 and b = 16


sum of the digits is a + b = 20 + 16 = 36


6 times 36 = 216.


number should be equal to 216 if the formula is true.


number is 10 * a + b = 10*20 + 16 = 200 + 16 = 216.


looks good.