A wealthy old woman died, and in her will she divided her fortune amongst her eight daughters. The total amount to be divided was less than 10000 ducats, and each daughter received a whole number of ducats according to the following:
The eldest daughter received 1/15 of the total.
The second daughter received 1/13 of what remained after the first daughter’s share was removed.
The third daughter received 1/11 of what remained after the previous daughters’ shares were taken.
The fourth daughter received 1/9 of what then remained.
The fifth daughter received 1/7 of what then remained.
The sixth daughter received 1/5 of what then remained.
The seventh daughter received 1/3 of what then remained.
Finally the youngest, favourite daughter received all of the remaining fortune.
How much did the youngest daughter receive?