SOLUTION: I'm a two-digit base-ten numeral. I am equal to six times the sum of my digits. Who am I?

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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