House floor ratio

The house has two floors. Men and women live on each floor in such a number that their ratio is 3:2 on each floor. Five more people live on the second floor than on the first floor. How many women live on the second floor?

Final Answer:

d =  24

Step-by-step explanation:

$$\begin{gathered} a:b=3:2 \\ c:d=3:2 \\ a+b+5=c+d \\ 2\cdot a=3\cdot b \\ 2\cdot c=3\cdot d \\ a+b+5=c+d \\ a>0 \\ c>0 \\ {a}_1=3,b_1=2,c_1=6,d_1=4 \\ {a}_2=6,b_2=4,c_2=9,d_2=6 \\ {a}_3=9,b_3=6,c_3=12,d_3=8 \\ {a}_4=12,b_4=8,c_4=15,d_4=10 \\ {a}_5=15,b_5=10,c_5=18,d_5=12 \\ {a}_6=18,b_6=12,c_6=21,d_6=14 \\ {a}_7=21,b_7=14,c_7=24,d_7=16 \\ {a}_8=24,b_8=16,c_8=27,d_8=18 \\ {a}_9=27,b_9=18,c_9=30,d_9=20 \\ {a}_{10}=30,b_{10}=20,c_{10}=33,d_{10}=22 \\ {a}_{11}=33,b_{11}=22,c_{11}=36,d_{11}=24 \\ d=24 \end{gathered}$$

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