Q:

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 dash half of the plants that he still​ had, plus 2 more.​ Finally, the thief leaves the nursery with 15 plants. How many plants were originally​ stolen?

Accepted Solution

A:
Answer:181 plants were originally stolen. Step-by-step explanation:To get the solution to this problem, We must go from the end to the beginning.When the thief left the nursery, he had 15 plants left. That is equivalent to half of the plants he gave to the third guard plus two more plants. That's:[tex]\frac{x_1}{2} +2 = 15[/tex]Where X3 is the amount of plants given to the 3rd. guardIsolating x3[tex]\frac{x_3}{2}=15-2[/tex][tex]\frac{x_3}{2}=13[/tex]X3= 26 plantsWhen the thief met the third guard, he had 26 plants. From this amount we can calculate the amount of plants that the thief had when he met the second guard. [tex]\frac{x_2}{2} +2 = 26[/tex]Where X2 is the amount of plants given to the 2nd. guardIsolating x2[tex]\frac{x_2}{2}=26-2[/tex][tex]\frac{x_2}{2}=24[/tex]X2= 48 plantsWhen the thief met the second guard, he had 48 plants. From this amount we can calculate the amount of plants that the thief had when he met the first guard. [tex]\frac{x_1}{2} +2 = 48[/tex]Where X1 is the amount of plants given to the 1st. guardIsolating x1[tex]\frac{x_1}{2}=48-2[/tex][tex]\frac{x_2}{2}=46[/tex]X1= 92 plantsSo, if we already know the amount of plants that the thief gave each guard, and also knowing that when he left the nursery he had 15 plants left, we can calculate the initial amount.[tex]X_i - X_1 -X_2-X_3=15[/tex]Where Xi is the initial amount of plants. Isolating Xi from the equation:[tex]X_i= 15+ X_1+X_2+X_3[/tex][tex]X_i=15+92+48+26[/tex][tex]X_i= 181[/tex]So, 181 plants were originally stolen.