The average height of a group of children would be increased by 5 cm if 10 of the children in the group were each 10 cm taller. How many children are in the group?
Let the total number of children =N
Let the average height of all N children =A
If 10 of the children were 10 cm taller =10*10 =100 cm
[N *A + 100] / N =[N * A] / N + 5, solve for N
[AN + 100]/N =A + 5
AN + 100 =N[A + 5]
AN + 100 =AN + 5N
5N = 100
N =100/5 = 20 - there were 20 kids.