Question

In the Itty Bitty High School, there are 85 students. There are 27 students who take French, 51 who take Geometry and 38 who take History. There are 10 that take Geometry and French, 7 that take History and French and 15 that take Geometry and History. There are 2 students who take all 3 and 5 that take none of these subjects.

Answer 1

58 students

Explanation:

Given

`Total = 85`

`French = 27`

`Geometry = 51`

`History = 38`

`None = 5`

`All = 2`

Required

Students that take only 1 subjects

The attached image illustrates the question.

For French only (x), we have:

`x + 7 -2+10-2+2=27`

`x + 15=27`

Collect like terms

`x =- 15+27`

`x =12`

For Geometry only (y), we have:

`y+10-2+15-2+2=51`

`y+23=51`

Collect like terms

`y=-23+51`

`y=28`

For History only (z), we have:

`z +15-2+7-2+2=38`

`z +20=38`

Collect like terms

`z =-20+38`

`z =18`

Students with one subject is then calculated as:

`1\ subject = x+y+z`

`1\ subject = 12 + 28 + 18`

`1\ subject = 58`