SOLUTION: Hi would you please help me with this word problem? A thief steals a number of plants from a nursery. On the way out he encounters three security guards, one after another. To

Question 133232: Hi would you please help me with this word problem?
A thief steals a number of plants from a nursery. On the way out he encounters three security guards, one after another. To each guard the thief is forced to give one half of the plants he still has plus two. Finally the thief leaves the nursery with one lone plant—how many plants were originally stolen?

Let x/2+2 be the plants given to the first guard
Let x/4+2 be the plants given to second guard
Let x/8+2 be the plants given to third guard

Multiply by LCD 8
4x+16-2x-16-x-16=8
x-16=8
x=24
check: (12+2)-(6+2)-(3+2)=1 OK
14+8+5+1= 28 plants stolen
But when you check the problem using 28 it does not work;
.5(28) +2 = 6, .5(16)+2=10, .5(10)+2= 7; 16+10+7=33+1=34

Found 3 solutions by oscargut, ptaylor, checkley71:
Answer by oscargut(891)   (Show Source):
You can put this solution on YOUR website!
First he gives x/2+2 (he has after that x/2-2)
he gives then (x/2-2)/2+2=x/4+1 (he has after that x/4-3)
he gives then (x/4-3)/2+2=x/8+1/2 (he has after that x/8-7/2
then x/8-7/2=1
then x/8=9/2
x=36

check:
gives 0.5(36)+2=20 then he has 16
gives 0.5(16)+2=10 then he has 6
gives 0.5(6)+2=5 then he has only 1 plant

Answer by ptaylor(2048)   (Show Source):
You can put this solution on YOUR website!
GOOD!!!!! YOU GAVE IT A SHOT
WHEN THE GUARD GIVES, YOU NEED TO KEEP TRACK OF WHAT HE HAS LEFT.
OK I FIND IT EASIER TO WORK THESE WORD PROBLEMS IF I CLEARLY LAY OUT WHAT THE UNKNOWNS REPRESENT, SO:
Let x= the number of plants originally stolen
The thief gives (x/2)+2 plants to the first guard
Thief then has x-((x/2)+2) or 2x/2-(x/2)-2 =(x/2)-2 plants left
Thief gives 1/2((x/2-2)+2) or (x/4)-1+2=(x/4)+1 to second guard
Thief then has ((x/2)-2)-((x/4)+1) or (x/2)-2-(x/4)-1=(x/4)-3 plants left
Thief gives 1/2((x/4)-3)+2 or (x/8)-(3/2)+2=(x/8)+1/2 to third guard
Thief has left ((x/4)-3)-((x/8)+1/2) and we are told that this equals 1, so:
(x/4)-3-(x/8)-1/2=1 multiply each term by 8
2x-24-x-4=8 simplify
x-28=8 add 28 to both sides
x-28+28=8+28
x=36-----------------number of pLAnts originally stolen
Ck
First guard
Gives 1/2(36)+2=18+2=20
Has left 36-20=16
Second guard
Gives 1/2(16)+2=10
Has left 16-10=6
Third guard
Gives 1/2(6)+2=5
Has left 6-5=1

Hope this helps----ptaylor

Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website!
THE EQUATION SHOULD BE:
X-(X/2+2)-(X/4+2)-(X/8+2)=1
YOU SHOULD START WITH THE TOTAL NUMBER OF PLANTS STOLEN WHICH IS X.
X-X/2-2-X/4-2-X/8-2=1
X-X/2-X/4-X/8=1+2+2+2 NOW COMBINE THE X TERMS USING A COMMON DENOMINATOR OF 8
(8X-4X-2X-1X)/8=7
X/8=7 NOW CRIOSS MULTIPLY
X=7*8
X=56 ANSWER FOR THE NUMBER OF PLANTS STOLEN.
PROOF:
56-(56/2=2)-(56/4+2)-(56/8+2)=1
56-28-2-14-2-7-2=1
56-55=1
1=1