## Algebra - Word problem (intermediate)?

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Divine
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### Algebra - Word problem (intermediate)?

Can someone help me sort this problem out as a formula, while explaining the reasoning? Also, could someone classify what kind of word problem this is? Thanks!

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?

stapel_eliz
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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?
It's probably simpler to just work backwards:

He ends with one.

He gave the last guy two, before which he must have had three. And this three was half of what he'd had before this last guy, so he must have had six when he left the second guy.

He gave the second guy two, before which he have had eight. And this eight was half of what he'd had before the second guy, so...

...and so forth.

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