Question

Every student in the senior class is taking history or science and 85 of them are taking both. If there are 106 seniors taking history and 109 seniors taking science, how many students are in the senior class?

Answer 1

130

Explanation:

Since 106 seniors are taking history and 109 seniors are taking science. If we add those numbers of seniors up we get 215, then we subtract the number of seniors that are taking both history and science because we counted them twice. So the total is 215 - 85 = 130. Therefore there are 130 students in the senior class.

Answer 2

Number of students in senior class is 130

Solution:

Given that Every student in the senior class is taking history or science

85 of them taking both history and science

106 seniors takes history

109 seniors takes science

To find: number of students in senior class

Let A be the set of the students of the senior class that take history

Let B be the set of students of senior class that they science

The number of students in senior class is given by:

`|A \cup B|=|A|+|B|-|A \cap B|`

Where,

A = 106 and B = 109 and |A n B| = 85

`|A \cup B|=106+109-85=130`

Thus number of students in senior class is 130