Answer:
14 students
Step-by-step explanation:
Given
Let:
[tex]b \to[/tex] read a book
[tex]t \to[/tex] watched TV
So, we have:
[tex]n = 50[/tex] -- total
[tex]b = 16[/tex]
[tex]t = 41[/tex]
[tex]none = 7[/tex]
Required
Students that did both (x)
This is calculated using:
[tex]Total = Books\ only + TV\ only + Both + None[/tex]
So, we have:
[tex]n = (b - x) + (t - x) + x + none[/tex]
This gives:
[tex]50 = (16 - x) + (41 - x) + x + 7[/tex]
Open brackets
[tex]50 = 16 - x + 41 - x + x + 7[/tex]
[tex]50 = 16 - x + 41 +7[/tex]
Collect like terms
[tex]x = 16 - 50 + 41 +7[/tex]
[tex]x = 14[/tex]
Hence, 14 students did both
