Problem 90 - College Algebra

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 initially stole 37 rare plants.

Step 1: Set Up the Problem

Let's call X the number of plants the thief initially stole. After meeting the first security guard, the thief gave half the plants, plus 2 more. So he was left with: X / 2 - 2 plants.

Step 2: Apply the Same Logic to Subsequent Security Guards

After giving plants to second and third guards, the number of plants would be halved and reduced by 2 each time. Representing those instances we get: ((X / 2 - 2) / 2 - 2) / 2 - 2 plants

Step 3: Create the Final Equation and Solve the Problem

After all these deductions, the thief was left with 1 plant. If we equate the above expression to 1, we get: ((X / 2 - 2) / 2 - 2) / 2 - 2 = 1. Solving this equation for X, X equals to 37. So the thief initially stole 37 plants.