Problem 72 - Algebra and Trigonometry

Question

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?

Step-by-Step Solution

Answer

The thief originally stole 36 rare plants.

Step 1: Identify the Final Number of Plants

The problem states that the thief is left with 1 plant. This is the final number of plants the thief has, so this is where the calculation will start.

Step 2: Apply Reverse Calculation for the First guard

Before he met the first guard, the thief had twice the plants plus two. According to the problem, the thief gave away half his plants plus 2 more to each guard, so if he had \( x \) plants before meeting the guard, then \( x/2 - 2 = 1 \), solving this equation gives, \( x = 6 \). So, the thief had 6 plants before meeting the first guard.

Step 3: Apply Reverse Calculation for the Second guard

Repeating this process for the second guard, if he had \( y \) plants before that, then \( y/2 - 2 = 6 \). Solving this equation gives \( y = 16 \). So, the thief had 16 plants before meeting the second guard.

Step 4: Apply Reverse Calculation for the Third guard

Repeating the process once again for the third guard, if he had \( z \) plants before that, then \( z/2 - 2 = 16 \). After solving this equation, \( z = 36 \). So, the number of plants the thief originally stole is 36.