Question

Some marbles are to be distributed among a group of children. It was observed that if 9 marbles are given to each child, then 3 children are left without any marbles and if 5 marbles are given to every child, then 5 marbles are left undistributed. What is the sum of the number of marbles and the number of children?

Answer 1

Solutions 

Let total number of children = x
Let total numbers if marbles = y

So,from árst condition , we get

y = 9 ( x - 3 )

y = 9x - 27
 
y -9x = -27 ------------------------------ ( 1 )

From second condition we get

y - 5 = 5x
 
y - 5x = 5 ----------------------------- ( 2 )

Now equation ( 2 ) - equation ( 1 ) , we get

4 x = 32

x = 8                        substitute that value in equation ( 2) we get

y - 40 = 5

y = 45 

Total number of marbles = 45 

Total number of children = 8 

Answer 2

Let total number of children = x 
Let total numbers if marbles = y 

So,from árst condition , we get 

y = 9 ( x - 3 ) 

y = 9x - 27
 
y -9x = -27 ------------------------------ ( 1 ) 

From second condition we get 

y - 5 = 5x
 
y - 5x = 5 ----------------------------- ( 2 ) 

Now equation ( 2 ) - equation ( 1 ) , we get 

4 x = 32 

x = 8                        substitute that value in equation ( 2) we get 

y - 40 = 5 

y = 45 

Total number of marbles = 45 

Total number of children = 8