The bottle

The bottle contains 1.5 liters of mineral water. Pour all the water from the bottle into empty cups with a volume of 1/3 l. We will fill all but one to the brim. What part of the volume of the last cup is filled with water?

Correct answer:

x =  1/2

Step-by-step explanation:

$$\begin{gathered} V_1=1.5\text{l} \\ {V}_2=1/3=\frac{1}{3}\doteq 0.3333\text{l} \\ n=V_1/V_2=1.5/0.3333=\frac{9}{2}=4\frac{1}{2}=4.5 \\ {n}_0=\lfloor n\rfloor =\lfloor 4.5\rfloor =4 \\ {V}_3=V_1-n_0\cdot V_2=1.5-4\cdot 0.3333=\frac{1}{6}\doteq 0.1667\text{l} \\ x=\frac{V_3}{V_2}=\frac{\frac{1}{6}}{\frac{1}{3}}=\frac{1}{2}=0.5 \end{gathered}$$

Try another example