Answer:
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
Step-by-step 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:
⇒ [tex]4x+5(x-20)=584[/tex]
⇒ [tex]4x+5x-100=584[/tex]
⇒ [tex]9x-100=584[/tex]
⇒ Adding 100 both sides.
⇒ [tex]9x-100+100=584+100[/tex]
⇒ [tex]9x=684[/tex]
⇒ Dividing 9 both sides.
⇒ [tex]x=\frac{684}{9}[/tex]
⇒ [tex]x=76[/tex] students.
Number of students in 5 of the grades were the students are fewer:
⇒ [tex]5(x-20)=5(76-20)=5(56)=280[/tex]
Total number of students in 5 of the grades = 280
