Use double false position to solve the following problem whi

Use double false position to solve the following problem, which is based on a problem in chapter 12 of Leonardo of Pisa\'s Liber Abbaci.^2 A certain man proceeding to Lucca on business to make a profit doubled his money, and he spent there 12 denari. He then left and went through Florence; he there doubled his money, and spent 12 denari. Then he returned to Pisa, doubled his money, and spent 12 denari. At the end of the three trips and after the expenses there will be 9 denari. It is sought how much he had at the beginning.

Solution

If he had x denari in the beginning;
After first trip = 2x-12
After second trip = 2(2x-12) -12 = 4x-36
After final trip = 2(4x-36) -12 = 8x-84
Now it is given that 8x-84=9 So 8x= 93; Hence x=93/8 = 11.625 denari

Thus at the beginning of the three trips he had 11.625 denari with him.