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?

The approach you suggest would work - as long as you find that only 1 of the situations is possible, and the other 3 aren't (like for example if someone has a non-integer/negative age, or you reach another contradiction of some sort).
On the other hand, you may find that there are several possibilities for which Josh's claims are false. But they may all give the same age for Beatrice which still enables you to answer the question. (Note that I haven't done the question so this may not be true at all)
