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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
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30000
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 .
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 .
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