Question

I can't figure out how to set up this problem...can anyone help me?

A thief steals a number of rare plants from a nursery. On the way out, the thief meets 3 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?

Answer 1

OK N = the number of original plants. Let w,x,y,z equal the thief and security guard number of plants in each's possession.
The theif has 1 plant so w=1.
Now our equation is:
1+ x +y + z = N
Let's do the # of plants that the first guard, x, gets:
'To each security guard, the thief is forced to give one-half the plants that he still has, plus 2 more. '
So I read this as...
x = N/2 + 2
Now our equation is
1 + (N/2+2) + y + z = N
Create a second equation for y...(it get's uglier)...
\[y=\Bigg [ \frac {N-\big ( \frac {N} {2} + 2 \big )} {2} + 2\Bigg ]\]

Answer 2

\[z= \bigg (\frac {N-y} {2}+2\bigg )\]

Answer 3

How did it go? Did you get it. Looks ugly doesn't it. BTW I worked backwards to check the answer N=36.