A container

A container with 2 1/2L of water is being poured into other containers that can hold 1 1/3L of water. Each container has to be filled, so how many L of water will the last container hold?

Correct answer:

x =  1 ¹⁄₆ = 7/6 l

Step-by-step explanation:

$$\begin{gathered} V=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2.5\text{l} \\ {V}_1=1\frac{1}{3}=1+\frac{1}{3}=\frac{1\cdot 3+1}{3}=\frac{3+1}{3}=\frac{4}{3}\doteq 1.3333\text{l} \\ n=V/V_1=\frac{5}{2}/\frac{4}{3}=\frac{5}{2}:\frac{4}{3}=\frac{5}{2}\cdot \frac{3}{4}=\frac{5\cdot 3}{2\cdot 4}=\frac{15}{8}=1.875 \\ {n}_1=\lfloor n\rfloor =\lfloor 1.875\rfloor =1 \\ x=V-n_1\cdot V_1=\frac{5}{2}-1\cdot \frac{4}{3}=\frac{7}{6}\text{l}=1\frac{1}{6}\text{l}=1.1667\text{l} \end{gathered}$$

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