Lemonade bottles

Three glasses are to be filled with lemonade. One can hold a quarter of a liter, the second a third of a liter, and the third 0.4 liters. How many 0.33l bottles will we need, and how much lemonade will be left in the last bottle? Express in fractions.

Final Answer:

n =  3
x =  0.0067 l

Step-by-step explanation:

$$\begin{gathered} V=1/4+1/3+0.4=\frac{59}{60}\doteq 0.9833\text{l} \\ {V}_1=0.33\text{l} \\ k=V/V_1=0.9833/0.33=\frac{295}{99}=2\frac{97}{99}\doteq 2.9798 \\ n=\lceil k\rceil =\lceil 2.9798\rceil =3 \end{gathered}$$

$x=n\cdot V_1-V=3\cdot 0.33-0.9833=\frac{1}{150}\text{l}=0.0067\text{l}$

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