Apartment Building Rooms

There are three sizes of apartments in the new building on the housing estate. One-sixth of the total number of apartments are four-room apartments, and one-third of the rest are two-room apartments. There are 160 three-room apartments. How many four-room and how many two-room apartments are there in the house?

Final Answer:

a =  30.0625
b =  -9.6875

Step-by-step explanation:

$$\begin{gathered} n/6+1/3\cdot (1-n/6)+160=n \\ 0.888889n=160.333333 \\ \frac{8}{9}n=\frac{481}{3} \\ 8n=1443 \\ n=1443/8=180.375 \\ a=n/6=180.375/6=\frac{481}{16}=30\frac{1}{16}=30.0625 \end{gathered}$$

n/6 + 1/3·(1-n/6) + 160 = n

5.333333n = 962


n = 962/5.33333333 = 180.375

n = 1443/8 = 180.375

Our simple equation calculator calculates it.

$b=1/3\cdot (1-n/6)=1/3\cdot (1-180.375/6)=-\frac{155}{16}=-9\frac{11}{16}=-9.6875$

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