Question

2 If a sum of money is divided equally among n children, each child will
receive $60. If another child is added to the group, and the sum is
divided equally among all the children, each child receives a $50 share.
What is the sum of money?​

Answer 1

Let x be the total sum of money divided among n children, then x/n =60 and x/(n+1) =50. We rearrange and make n the subject n=x/60. Now substitute n=x/60 in x/(n+1) and get x=50x/60 +50. We have x-50x/60 =50

That is x/6 = 50, therefore x =300. The sum of money is $300 and is divided among 5 children where each gets $60. If another child is added total number of children is 6 so each child gets $50.