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# Counting Problems and Trees

In one residence, cell phones, lap top computers and digital tvs are very popular among students. In fact, all of the students own atleast one of these items, although onlu 15 own all 3. Cell phones are the most popular with twice as many students owning cell phones as own lap tops. and digital tvs are still rare, since only half as many students own these as own laptops. As it happens all students who own a digital laptop also have a cellphone.

If there are 10 students who own both a cellphone and a digital tv, but not a laptop, and there are 20 students who don't own a cellphone, how many student live in the residence?

#### Solution Preview

If we can figure out how many tvs exist in the dorm, then we've got the problem solved. We know that 15 students own all three devices. That means that there are at least 15 tvs in the dorm. We also know that 10 students own a cell and a tv (but not a laptop). That means that these 10 tvs are not included in the 15 tvs at the beginning (since these 15 students do not have a laptop), right? Got it? Now, we're up to 25 tvs. ...

#### Solution Summary

A counting problem is solved.

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