Yasmine makes her own chocolate beverage by mixing volumes of milk and syrup in the ratio $5: 2$. Milk comes in $2 \mathrm{~L}$ bottles and syrup comes in $1.4 \mathrm{~L}$ bottles. Yasmine has a limitless supply of full bottles of milk and of syrup. Determine the smallest volume of chocolate beverage that Yasmine can make that uses only whole bottles of both milk and syrup.
Suppose that Yasmine uses $m$ full bottles of milk and $s$ full bottles of syrup.

The volume of milk that she uses is thus $2 m \mathrm{~L}$ and the volume of syrup that she uses is $1.4 s \mathrm{~L}$.

For this ratio to equal $5: 2$, we need $\frac{2 m}{1.4 s}=\frac{5}{2}$ or $4 m=7 s$.

Since 4 and 7 have no common divisor larger than 1, then the smallest positive integers that satisfy this are $m=7$ and $s=4$.

Thus, the volume, in litres, of chocolate beverage that Yasmine makes is $2 \cdot 7+1.4 \cdot 4=19.6$.

ANSWER: $19.6 \mathrm{~L}$