One day all of Mrs. Brown's grandchildren came to visit her.
There was a bowl of apples and pears on the kitchen table.
Mrs. Brown gave each child the same number of pieces of fruit
without keeping track of which kind.
Bobby got 1/8 of all the apples and 1/10 of all the pears.
How many grandchildren did Mrs. Brown have?
Well, if there are 8 apples and 10 pears, then Bobby gets 2 pieces of fruit and there are 18/2 = 9 grandchildren altogether.
Is 9 the only solution?
Well, Let there be 8x apples and 10y pears, where x and y are positive integers.
Then, Bobby gets x+y pieces, and the number of grandchildren = (8x + 10y)/(x+y) = 8 + 2y(x+y).
This must be an integer, which can only be the case if x = y.
So the number of grandchildren must be 8 + 2y/2y = 9
Edited on August 27, 2015, 4:25 pm
Algebraic solution (spoiler)
