Question

50 students were asked what they did last night. 16 said they read a book, 41 said they watched TV, 7 said they did neither, how many students did both​

Answer 1

14 students

Explanation:

Given

Let:

`b \to` read a book

`t \to` watched TV

So, we have:

`n = 50` -- total

`b = 16`

`t = 41`

`none = 7`

Required

Students that did both (x)

This is calculated using:

`Total = Books\ only + TV\ only + Both + None`

So, we have:

`n = (b - x) + (t - x) + x + none`

This gives:

`50 = (16 - x) + (41 - x) + x + 7`

Open brackets

`50 = 16 - x + 41 - x + x + 7`

`50 = 16 - x + 41 +7`

Collect like terms

`x = 16 - 50 + 41 +7`

`x = 14`

Hence, 14 students did both