Question 271715
A thief steals a number of rare plants from a nursery. On his way out, the thief meets three security guards, one after another. To each security guard the thief is forced to give one-half the plants that he still has, plus two more. Finally, the thief leaves the nursery with no plants. How many plants were originally stolen?

x plants stolen
x - (1/2 * x + 2) 1st guard
x/2 - 2 after 1st guard
x/2 - 2 - (1/2 * (x/2 - 2) + 2) 2nd guard
x/2 - 2 - (x/4 - 1 + 2)
x/2 - 2 - x/4 - 1
2x/4  - x/4 - 3
x/4 - 3 after 2nd guard
x/4 - 3 - (1/2 * (x/4 - 3) + 2) 3rd guard
x/4 - 3 - (x/8 - 3/2 + 2)
2x/8 - 3 - (x/8 + 1/2)
2x/8 - 3 - x/8 - 1/2
x/8 - 7/2 after 3rd guard

x/8 - 7/2 = 0
x/8 = 7/2
x = 7/2 * 8
x = 56/2 = 28 plants originally stolen

check: 28
       28 - 16 = 12 after 1st guard
       12 - 8 = 4 after second guard
       4 - 4 = 0 after 3rd guard