Four statements, One statement is false math problem When trying to recall some facts about the ages of his three aunts, Josh made the
following claims:


*

*Alice is fifteen years younger than twice Catherine’s age.

*Beatrice is twelve years older than half of Alice’s age.

*Catherine is eight years younger than Beatrice.

*The three women’s ages add to exactly one-hundred years.


However, Josh’s memory is not perfect, and in fact only three of these four
claims are true. If each aunt’s age is an integer number of years, how old is
Beatrice?
I have these following equations:
$a=2c-15$ 
$b=\frac12 a +12$ 
$c=b-8$
$a+b+c=100$
How would I solve this problem? Do I assume one statement at a time is false and try the situations one by one?

Or simply do it case by case.
Case 1:1 is true.
a=2c-15.
Case 1a:2 is true
b=1/2 a + 12 = c - 7 1/2 + 12.  A contradiction.
Case 1b: 2 is false, 3 and 4 are true
c= b-8
a+b+c =100 so 2c-15 + c + 8 + c =4c - 7 = 100 so 4c = 107.  A contradiction.
Case  2: 1 is false, all others true.  Only case left.
b=1/2 a +12
c= b-8 = 1/2  a +4
a + b+c=2a +16=100
a= 42; b=33;c=25.
