## Task 3 - 050923

A brother says to his sister:

"When Aunt Katja was as old as we both are together now, you were as old as I am now.

But when Aunt Katja was as old as you are now, you were... ."

a) How old was the sister then?

b) How many times older than the sister is Aunt Katja now?
Sizes: $b=$ current age of the brother, $s=$ current age of the sister, $t=$ current age of the aunt. "When Aunt Katja was as old as we both are together now, you were as old as I am now" means

$$
s-(t-(b+s))=b \Rightarrow t=2 s
$$

"But when Aunt Katja was as old as you are now, you were... ." results in

$$
s-(t-s)=s-(2 s-s)=s-s=0
$$

a) The sister was just born.

b) The aunt is now twice as old as the sister.