A man left 6M to his children and grandchildren, 7 in all. The children received 1/3 of it which is 200,000 more a piece than what each of the grandchildren received. How many children were there?

Answer 1

children --- x
grandkids --- 7-x

children got (1/3)(6,000,000) = 2,000,000
so grandkids got 4,000,000

each grandkid got 4000000/(7-x)
kids got 2000000/x each

"200,000 more a piece than what each of the grandchildren"
---> 2000000/x - 200000 = 4000000/(7-x)
times x(7-x)
2000000(7-x) - 200000x(7-x) = 4000000x
divide by 200000
10(7-x) - x(7-x) = 20x
70 - 10x - 7x + x^2 - 20x = 0
x^2 - 37x + 70 = 0
(x - 2)(x - 35) = 0
x = 2 or x = 35 , the latter obviously not acceptable

There were 2 children and 5 grandchildren

check:
kids got 2,000,000/2 or 1 M each
grandkids got 4,000,000/5 or 800,000 each

so each kid got 200,000 more than each grandchild
My answer is correct

Answer 2

Thank you so much. That 200,000 thingy confused me so I had a hard time making my equation. Thanks for the help!