Question

A school has 9 grades and 5 of the grades have 20 fewer students than the other 4. The school has 585 students. How many students are in the 5 with fewer students?

Answer 1

A school has 9 grades and 5 of the grades have 20 fewer students than the other 4. The school has 584 students. How many students are in the 5 with fewer students?

Total number of students in 5 of the grades = 280

Explanation:

Let the number of students in each of (other 4) grades be 'x'

There are 4 grades so total no. of students in (other 4) = 4x

Now

Number of students in each (5 of the grades) = (x-20)

Total number of student in (5 of the grades) = 5(x-20)

According to the question:

⇒
`4x+5(x-20)=584`

⇒
`4x+5x-100=584`

⇒
`9x-100=584`

⇒ Adding 100 both sides.

⇒
`9x-100+100=584+100`

⇒
`9x=684`

⇒ Dividing 9 both sides.

⇒
`x=(684)/(9)`

⇒
`x=76` students.

Number of students in 5 of the grades were the students are fewer:

⇒
`5(x-20)=5(76-20)=5(56)=280`

Total number of students in 5 of the grades = 280