In a certain two \(65 \%\) families own cell phones, 15000 families own scooter and 15\% families own both. Taking into consideration that the families own at least one of the two, the total number of families in the town is

Let the total number of families be \(x\).
Let \(A=\) number of families that own cell phones \(n(A)=\frac{65}{100} \times x\)
Let \(B=\) number of families that own scooter \(n(B)=15000\)
and \((A \cap B)=\) number of families that own cell phones and scooter both
\(n(A \cap B)=\frac{15}{100} \times x\)
Here, \(n(A \cup B)=x\)
\(n(A \cup B)=n(A)+n(B)-n(A \cap B)\)
\(x=\frac{65 x}{100}+15000-\frac{15 x}{100}\)
\(\begin{aligned} \Rightarrow & & 100 x &=65 x+1500000-15 x \\ \Rightarrow & & 100 x-50 x &=1500000 \\ \Rightarrow & & 50 x &=1500000 \\ \Rightarrow & & x &=30000 \end{aligned}\)
Total number of families in the town is 30000 .