Solution to in a village, 180 houses have TV, 120 houses have radio. 80 houses have both. … - Sikademy
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Archangel Macsika

in a village, 180 houses have TV, 120 houses have radio. 80 houses have both. 125 houses have nothing. Find total number of houses

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Solution. A set of houses who have a TV include a set of houses who have a TV and radio. Therefore, a set of houses who have only a TV


180-80=100

A set of houses who have a radio include a set of houses who have a TV and radio. Therefore, a set of houses who have only a radio


120-80=40

It has four sets that do not have common elements since the conditions for including elements in sets are mutually exclusive. (houses who have only a TV; houses who have only a radio; houses have nothing; houses have both TV and radio).

Therefore the total number of houses is equal to


100+40+125+80=345

Answer. 345 houses

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