Math Challenges

Submissions for Problem #22

Problem #22

A cable company offers its 10,000 customers two specialized services: high-speed internet and digital telephone. If 3,770 customers use high-speed internet, 3,250 use digital telephone, and 4,530 do not use either of these services, how many customers use both high-speed internet and digital telephone?

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zapwai

Solution: \( \displaylines{n\left(I\cup T\right)=n\left(I\right)+n\left(T\right)-n\left(I\cap T\right)\\ 5470=3770+3250-n\left(I\cap T\right)\Rightarrow n\left(I\cap T\right)=1550} \)