In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is
Step-by-Step Solution
Key Concept: Venn diagram problems require identifying disjoint regions and using their percentages to set up equations relating parts to the whole.
Let the total population of town be $x$. From the Venn diagram, 20% use Phone only, 5% use both, and 10% use Scooter only, totaling 35%. Therefore, 65% use neither. Setting up the equation: $\frac{20x}{100} + \frac{5x}{100} + \frac{10x}{100} + \frac{65x}{100} = x$. The users (Phone or Scooter) represent 35% of the population: $\frac{35x}{100} = 1500$. Solving: $x = \frac{1500 \times 100}{35} = \frac{150000}{5} = 30000$.
Correct Answer: 30000