Salesman 4

The salesman sold 3/5 of the potatoes on the first day and 2/3 of the rest on the second day. What fraction of the potatoes did he sell in two days? What fraction of the potatoes did he have left?

Correct answer:

x =  13/15
z₂ =  2/15

Step-by-step explanation:

$$\begin{gathered} a=\frac{3}{5}=0.6 \\ {z}_1=1-a=1-\frac{3}{5}=\frac{1\cdot 5}{5}-\frac{3}{5}=\frac{5}{5}-\frac{3}{5}=\frac{5-3}{5}=\frac{2}{5}=0.4 \\ b=\frac{2}{3}\cdot z_1=\frac{2}{3}\cdot \frac{2}{5}=\frac{2\cdot 2}{3\cdot 5}=\frac{4}{15}\doteq 0.2667 \\ x=a+b=\frac{3}{5}+\frac{4}{15}=\frac{9}{15}+\frac{4}{15}=\frac{9+4}{15}=\frac{13}{15}=0.8667 \end{gathered}$$

$z_2=1-x=1-\frac{13}{15}=\frac{1\cdot 15}{15}-\frac{13}{15}=\frac{15}{15}-\frac{13}{15}=\frac{15-13}{15}=\frac{2}{15}=0.1333$

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