SOLUTION: A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to gi

Question 145989This question is from textbook Thinking Mathematically
: A thief steals a number of rare plants from a nursery. On the 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 2 more. Finally, the thief leaves the nursery with 1 lone palm. How many plants were originally stolen? I did this one, but I am not sure if it was done correctly. My answer is 76. Sometimes I think I over think the problem.
Thank you for your help!! This question is from textbook Thinking Mathematically

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A thief steals a number of rare plants from a nursery. On the 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 2 more. Finally, the thief leaves the nursery with 1 lone palm. How many plants were originally stolen? I did this one, but I am not sure if it was done correctly. My answer is 76. Sometimes I think I over think the problem.
:
Let x = no. of plants stolen
:
After the 1st guard:
x - (.5x+2)
x -.5x - 2
.5x-2 plants left
:
After the 2nd guard
(.5x-2) - (.5(.5x-2)+2)
.5x - 2 - (.25x-1+2)
.5x - 2 - (.25x+1)
.5x - 2 - .25x - 1
.25x - 3 plants left
:
After the 3rd guard
(.25x-3) - (.5(.25x-3)+2) = 1
.25x - 3 - (.125x-1.5+2) = 1
.25x - 3 -(.125x+.5) = 1
.25x - 3 -.125x -.5 = 1
.125x - 3.5 = 1
.125x = 1 + 3.5
x =
x = 36 plants
:
Check solution
36 - 20 = 16
16 - 10 = 6
6 - 5 = 1
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