SOLUTION: On Christmas Eve a large family gathers at Grandpa Pennywise�s mansion. Every year he gives money to his grandchildren. They way he distributes the money, however, is a bit eccent

Question 516633: On Christmas Eve a large family gathers at Grandpa Pennywise�s mansion. Every year he gives money to his grandchildren. They way he distributes the money, however, is a bit eccentric. Grandpa Pennywise gives each grandson the amount of money that equals the number grandsons he has. He also does the same thing with the granddaughters as well. Last year, the number of girls equaled one less than the number of boys. This year the girls are excited because this past year newborn twin girls were born which would allow them to finally receive more money than the boys. This year Grandpa Pennywise gave a total of $841 to his grandchildren. How much did he give to the grandsons? How many grandchildren does he have?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We can see that the amount of money he gives to his grandsons is a perfect square, same thing with his grand-daughters. Let x be the number of grandsons. Then he has x+1 grand-daughters because there is one more grand-daughter than grand-son. Also,

so we can solve for x and be done. We can either solve it algebraically, or note that 841 = 29^2, and there is a 20-21-29 Pythagorean triple. Hence, there are 20 grand-sons and 21 grand-daughters so he gave 20^2 = $400 to his grandsons, and he has 41 grand-children.

Update: 20-21-29 is a Pythagorean triple because 20^2 + 21^2 = 29^2 (hence we can let x = 20).
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