Sales stores

The first sales store passed the 1/3 and the second 2/5 of the total amount of goods. In the third store passed the 2/3 rest of the goods. The remaining 40 kg of goods put into fourth store. How many kilograms of goods pass to a third store?

Final Answer:

c =  80 kg

Step-by-step explanation:

$$\begin{gathered} r_{12}=\frac{1}{3}+\frac{2}{5}=\frac{5}{15}+\frac{6}{15}=\frac{5+6}{15}=\frac{11}{15}\doteq 0.7333 \\ {r}_3=\frac{2}{3}\cdot (1-r_{12})=\frac{2}{3}\cdot (1-\frac{11}{15})=\frac{8}{45}\doteq 0.1778 \\ {r}_{123}=r_{12}+r_3=\frac{11}{15}+\frac{8}{45}=\frac{33}{45}+\frac{8}{45}=\frac{33+8}{45}=\frac{41}{45}\doteq 0.9111 \\ {r}_{123}\cdot x+40=x \\ 0.91111111111111\cdot x+40=x \\ 0.088889x=40 \\ x=\frac{40}{0.08888889}=450 \\ x=450 \\ c=r_3\cdot x=\frac{8}{45}\cdot 450=\frac{8\cdot 450}{45}=\frac{3600}{45}=80\text{kg} \end{gathered}$$

Try another example