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Question 335162: I'm a two-digit base-ten numeral. I am equal to six times the sum of my digits. Who am I?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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