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Fibonacci's Problem 4.

I have worked this problem out many times and always end up with the answer of 7 sons and 49 bezants, but that is incorrect. Here is the question:

A man left to his oldest son one bezant a seventh of what was left; then, from the remainder, to his next son he left two bezants and a seventh of what was left; then from the remainder, to his third son he left three bezants and a seventh of what was left. He continued in this way, giving each son one bezant more than the previous son and a seventh of what remained. By this division it developed that the last son received all that was left and all the sons shared equally. How many sons were there and how large was the man's estate?

If you could help me to figure this out it would be very much appreciated. : ) thank you!
Sep 17 '09 #1
6 2968
Banfa
9,065 Expert Mod 8TB
I am not sure how you get to 7 sons and 49 bezants, that fails on the first step

1 + 1/7 of whats left = 1 + 1/7 * (49 - 1)

But 49 - 1 is not divisible by 7.

The final answer must be a multiple of 7 plus 1 for the first stage to work

At the 2nd stage the calculation is

2 + 1/7 of what's left = or 2 + 1/7(N' - 2)

where N' is what is left after the first stage therefore the amount left after the first stage must be a multiple of 7 plus 2.

A little trial and error (or a google search) should lead you to the right answer.
Sep 17 '09 #2
I don't believe i had the correct equation in my mind when I first started doing this problem, which is how I recieved my incorrect answer. I am still not understading the way to receive the correct answer.... I understand how you get the equation now, but past that I am confused.
Sep 18 '09 #3
ok i think i figured it out. I guessed and checked and i believe the answere is 6sons and 36 bezants?
Sep 29 '09 #4
Banfa
9,065 Expert Mod 8TB
That is the answer I got.
Sep 29 '09 #5
Cool! Thanks so much for the help!! I couldn't have done it without the equation you gave me!! :)
Sep 30 '09 #6
tlhintoq
3,525 Expert 2GB
Just a reminder...
Bytes is not a homework help website and we even have guidelines about doing student's homework.
http://bytes.com/faq.php?faq=posting..._or_coursework
Oct 12 '09 #7

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