The painter

Alex had 5/6 liter of white paint. He used 1/8 of it to paint the walls and 2/5 of the remaining to paint the fence. How much paint is left?

Correct answer:

x =  13/24 l

Step-by-step explanation:

$$\begin{gathered} V=\frac{5}{6}\doteq 0.8333\text{l} \\ b=1-\frac{1}{8}=\frac{1\cdot 8}{8}-\frac{1}{8}=\frac{8}{8}-\frac{1}{8}=\frac{8-1}{8}=\frac{7}{8}=0.875 \\ c=\frac{2}{5}\cdot b=\frac{2}{5}\cdot \frac{7}{8}=\frac{2\cdot 7}{5\cdot 8}=\frac{14}{40}=\frac{7}{20}=0.35 \\ d=1-c=1-\frac{7}{20}=\frac{1\cdot 20}{20}-\frac{7}{20}=\frac{20}{20}-\frac{7}{20}=\frac{20-7}{20}=\frac{13}{20}=0.65 \\ x=V\cdot d=\frac{5}{6}\cdot \frac{13}{20}=\frac{5\cdot 13}{6\cdot 20}=\frac{65}{120}=\frac{13}{24}\text{l}=0.5417\text{l} \end{gathered}$$

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