Question 93
Anna, Berta and Carol make fruit drinks from syrup. Anna makes $a$ litres of drink by mixing water and syrup in the proportion of $a : 1$. Berta makes $b$ litres of drink by mixing water and syrup in the proportion of $b : 1$. Carol makes $c$ litres of drink by mixing water and syrup in the proportion of $c : 1$. (It is not known if $a$, $b$ and $c$ are integers.) They make $6$ litres of drink in total. Prove that they use at most $2$ litres of syrup.