Sand in the warehouse

Several tonnes of sand were delivered to a building materials warehouse in the morning. The first customer, Adamík, took away five sixths of it. The second customer, Bílý, bought two thirds of the remainder, and the last customer, Certis, took away three fifths of what was left. In the evening, 80 kg of sand remained in the warehouse. How many tonnes of sand were in the warehouse in the morning? How many kilograms of sand did each customer buy?

Final Answer:

x =  3.6 t
a =  3000 kg
b =  400 kg
c =  120 kg

Step-by-step explanation:

$$\begin{gathered} 5/6x+2/3\cdot (x-5/6x)+3/5\cdot (x-(5/6x+2/3\cdot (x-5/6x)))+0.080=x \\ 5/6\cdot x+2/3\cdot (x-5/6\cdot x)+3/5\cdot (x-(5/6\cdot x+2/3\cdot (x-5/6\cdot x)))+0.080=x \\ 0.666667x=2.4 \\ x=\frac{2.4}{0.66666667}=3.6 \\ x=\frac{18}{5}=3.6=\frac{18}{5}\text{t}=3.6\text{t} \end{gathered}$$

$$\begin{gathered} x_2=x\to \text{kg}=x\cdot 1000\text{kg}=3.6\cdot 1000\text{kg}=3600\text{kg} \\ a=\frac{5}{6}\cdot x_2=\frac{5}{6}\cdot 3600=\frac{5\cdot 3600}{6}=\frac{18000}{6}=3000\text{kg} \end{gathered}$$

$b=\frac{2}{3}\cdot (x_2-a)=\frac{2}{3}\cdot (3600-3000)=400\text{kg}$

$c=\frac{3}{5}\cdot (x_2-a-b)=\frac{3}{5}\cdot (3600-3000-400)=120\text{kg}$

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