Question

Of $650$ cities surveyed, each city had an art museum, or a nature museum, or both. Of the $320$ cities that had art museums, $\frac{1}{4}$ also had nature museums. What is the total number of cities surveyed that had nature museums?

Answer 1

Total number of cities are $650$.

Number of cities that had art museum are $320$.

$\therefore$ number of cities that had only nature museums $=650-320=330$

Number of cities that had both art and nature museums are $\frac{1}{4}\times 320=80$.

Therefore the number of cities that had nature museums are $330+80=410$.