Tax assessments

A courier delivered new real estate tax assessments to citizens in the form of mail letters. Two fifths of the letters he delivered to citizens at their permanent residence, two thirds of the remaining letters he delivered to citizens at another contact address, and 192 letters he left at the post office because he did not reach the addressees. How many letter deliveries did he deliver to the permanent residence address and how many to another contact address?

Final Answer:

a =  384
b =  384

Step-by-step explanation:

$$\begin{gathered} r_1=\frac{2}{5}=0.4 \\ {r}_2=1-r_1=1-\frac{2}{5}=\frac{1\cdot 5}{5}-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}=0.6 \\ {r}_3=\frac{2}{3}\cdot r_2=\frac{2}{3}\cdot \frac{3}{5}=\frac{2\cdot 3}{3\cdot 5}=\frac{6}{15}=\frac{2}{5}=0.4 \\ {r}_1\cdot n+r_3\cdot n+192=n \\ 0.4\cdot n+0.4\cdot n+192=n \\ 0.2n=192 \\ n=\frac{192}{0.2}=960 \\ n=960 \\ a=r_1\cdot n=0.4\cdot 960=384 \end{gathered}$$

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