Problem 90 - College Algebra Essentials

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 46 plants.

Step 1: Work backwards from the final amount

The thief leaves with 1 plant. To find out what he had before giving plants to the third security guard, remember that the thief gave him half the plants plus 2, therefore this amount is half of what he had before meeting him. Considering this, we have to subtract the 2 plants given away and then multiply by 2. This will give us the amount of plants the thief had before meeting the third guard.

Step 2: Determine plants before meeting the second guard

By applying the same logic as in step 1 to the amount found previously, we can determine the number of plants before the thief met the second guard. Subtract the 2 plants given away and then multiply by 2.

Step 3: Determine original number of plants

Again, apply the same logic to the amount determined in step 2. The thief had to have twice the plants plus 2 to give the first guard half his plants plus 2. This will result in the original number of plants stolen.