SOLUTION: Three years ago, my age was a prime number. • This year, my age is a multiple of 4. I have a brother whose age twenty years ago was half my current age. • The sum of t

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Question 1081102: Three years ago, my age was a prime number.
• This year, my age is a multiple of 4.
I have a brother whose age twenty years ago was
half my current age.
• The sum of the digits of my age is equal to one
more than the product of the digits.
What is my age?
What is my brother’s age?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
• The sum of the digits of my age is equal to one
more than the product of the digits. 

t = the tens digit of my age
u = the ones or units digit of my age

t+u = tu+1
t-tu = 1-u
t(1-u)=1-u
t=(1-u)/(1-u)
t=1

So the tens digit is 1.

• This year, my age is a multiple of 4. 
So my age is either 12 or 16, since those are the only
two-digit multiples of 4 with tens digit 1.

• Three years ago, my age was a prime number.
I can't be 12, for if I were, three years ago I would have been 9,
but 9 is not a prime number.  So I must be 16, for 3 years ago I
was 13, which is a prime number.

So my age is 16.

• I have a brother whose age twenty years ago was
half my current age.
Half my age is 8, so for my brother to have been 8 years old 20 
years ago, he must now be 8+20 or 28.

Edwin