300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would hace received one apple less. Find the number of students.
300 apples are distributed equally among a certain number of students. Had there been 10 more students, each would hace received one apple less. Find the number of students.
Let the total number of students= x
Total number of Apples= 300
1st case:
Number of apples received by each student= 300/x
2nd case:
In this case number of boys increased (x+10)
Number of Apples received by each boy= 300/(x+10)
A.T.Q
(300/x) -1 = 300/(x+10)
300/x -300/(x+10) =1
Lcm = x(x+10)
300(x+10) - 300x/( x(x+10)) = 1
300x+3000-300x = x(x+10)
3000= x²+10x
x²+10x-3000=0
[ Factorization by middle term splitting]
x²+60x-50x-3000=0
x(x+60)- 50(x+60)=0
(x+60)(x-50)=0
x+60=0,. x=-60
x-50=0
x= 50
Therefore,x= -60 cannot be taken as Number of students are always positive.
Hence, the total number of students in the class= 50
Let the total number of students= x
Total number of Apples= 300
1st case:
Number of apples received by each student= 300/x
2nd case:
In this case number of boys increased (x+10)
Number of Apples received by each boy= 300/(x+10)
A.T.Q
(300/x) -1 = 300/(x+10)
300/x -300/(x+10) =1
Lcm = x(x+10)
300(x+10) - 300x/( x(x+10)) = 1
300x+3000-300x = x(x+10)
3000= x²+10x
x²+10x-3000=0
[ Factorization by middle term splitting]
x²+60x-50x-3000=0
x(x+60)- 50(x+60)=0
(x+60)(x-50)=0
x+60=0,. x=-60
x-50=0
x= 50
Therefore,x= -60 cannot be taken as Number of students are always positive.
Hence, the total number of students in the class= 50
