Apartment sizes

The house has apartments of three sizes. One-sixth are four-room, and one-third are two-room. There are 160 three-room apartments. How many two-room apartments are there?

Final Answer:

a =  80
b =  48

Step-by-step explanation:

$$\begin{gathered} p_4=1/6=\frac{1}{6}\doteq 0.1667 \\ {p}_2=1/3\cdot (1-p_4)=1/3\cdot (1-0.1667)=\frac{5}{18}\doteq 0.2778 \\ {p}_3=1-(p_2+p_4)=1-(0.2778+0.1667)=\frac{5}{9}\doteq 0.5556 \\ n=160/p_3=160/0.5556=288 \\ a=p_2\cdot n=0.2778\cdot 288=80 \end{gathered}$$

$b=p_4\cdot n=0.1667\cdot 288=48$

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