Question

A merchant doing business in Lucca doubled his money there and then spent 12 denarii. On leaving, he went to Florence, where he also doubled his money and spent 12 denarii. Returning home to Pisa, he there doubled his money and again spent 12 denarii, nothing remaining. How much did he have in the beginning?

Answer 1

10.5 denarii

Explanation:

Step 1: Initially Doubled his money in Lucca and spent 12 denarii

Let's assume the initial money he had before he did anything with it is x,

meaning if he doubled it in Lucca he would have (2×x)=2x, he then spent 12 denarii meaning he was left with (2x-12) denarii.

Step 2: In Florence he doubled what was left on leaving Lucca and spent 12

This is expressed as 2(2x-12)-12=4x-24-12=4x-36

(4x-36) denarii is what remained after he left Florence to Pisa

Step 3: In Pisa he doubled what was left on leaving Florence and spent 12 denarii

This is expressed as 2(4x-36)-12=8x-72-12=8x-84

Step 4: After getting back home in Pisa he was left with nothing

This is expressed as; 8x-84=0, 8x=84

solving for x by dividing both sides of the equation by 8

8x/8=84/8

x=10.5 denarii