GMAT Math

A castle in the faraway land of Aluossim was surrounded by four moats. One day, the castle was attacked and captured by a fierce tribe from the north. Guards were stationed at each bridge. Prince Juan was allowed to take a number of bags of gold from the castle as he went into exile. However, the guard at the first bridge demanded half the bags of gold plus one more bag. Juan met this demand and proceeded to the next bridge. The guards at the second, third, and fourth bridges made identical demands, all of which the prince met. When Juan finally crossed all the bridges, a single bag of gold was left. With how many bags did Juan start?

Backsolving
after 4th gate Juan had one bag
before 4th gate x , x-x/2-1= 1 , x = 4
before 3 gate , x-x/2-1 = 4 , x = 10
2 gate 22. 1st gate 46

easier if options are given

if x bags at first gate
then number of bags at 4th gate = (x/16 -7/8) -1 which is equal to 1 because Juan remains with 1 bag at the 4th gate
Solving for x , x =46

@kstv - your's is a much easier approach - the backsolving process

I started from Gate 1 rather than work backwards from Gate 4.

I don't get it, can you please explain ?

Thank you guys