Of 100 clock radios with digital tuners and / or CD players sold recently in a department store, 70 had digital; tuners and 90 and CD players. How many radios had both digital tuners and CD players? ... ?

Question

Mathematics

Johanna Mcknight

13 July, 08:23

Of 100 clock radios with digital tuners and / or CD players sold recently in a department store, 70 had digital; tuners and 90 and CD players. How many radios had both digital tuners and CD players? ... ?

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Answers (1)

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Abraham Mills · Answer 1

The answer is 60.

Let A be the number of radios with digital tuners and let B be the number of radios with CD players.

The total number of radios is A∪B. It consists of both A radios and B radios, but however, radios with both digital tuners and CD players (A∩B) must be excluded from that number (either way they will be counted twice):

A∪B = A + B - A∩B

A∪B = 100

A = 70

B = 90

A∩B = ?

100 = 70 + 90 - A∩B

100 = 160 - A∩B

A∩B = 160 - 100

A∩B = 60