Question

There are five thieves, each loot a bakery one after the other such that the first one takes 1/2 of the total no. of the breads plus 1/2 of a bread. Similarly 2nd, 3rd,4th and 5fth also did the same. After the fifth one no. of breads remained are 3. Initially how many breads were there?

Answer 1

x is number of breads

Answer 2

total - breads taken=3

Answer 3

i want to know that how much 1/2 of bread contributes to total number of breads

Answer 4

Alright @nitz I can teach you how to do this but you'll have listen (follow instructions) carefully and not interrupt me by typing while I am, and also answer my questions. Are you willing to do that and learn?

Answer 5

here is the equation
X-(5X/2+5/2X)=3

Answer 6

solve it

Answer 7

Please stop giving out answers @Fazeelayaz and that's wrong anyway!

Answer 8

@nitz do you want to learn or not. If not then that's fine, there are plenty of other people I can teach. If yes then you need to reply to my post above.

Answer 9

plz tell me

Answer 10

total -breads taken=3 is that correct?

Answer 11

OK @Fazeelayaz but as I told @nitz earlier you'll have listen (follow instructions) carefully and not interrupt me by typing while I am, and also answer my questions. Are you willing to do that and learn? And no that is not correct! Now are you willing to learn or not?

Answer 12

oh yes plz do it fast i am hungry

Answer 13

No! Proper learning and understanding cannot be rushed. Hence I'll ask one final time, do you or anyone else viewing this want to learn or not?!

Answer 14

yes plz plz plz

Answer 15

yes please

Answer 16

plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answer 17

OK @Fazeelayaz and @nitz first as you correctly said at the beginning, let x represent the number of breads that were initially present. Now we shall approach this problem one step at a time. A step for each of the five thieves.

Step 1: Thief #1

If there are initially x breads, and the 1st thief takes half of these plus half of one bread, then what is the expression that represents the number of breads that remain after this first action?

Answer 18

X-(X/2+1/2X)

Answer 19

x/2-1/2

Answer 20

x-(1/2)x+(1/2)

Answer 21

in brackets x/2-1/2

Answer 22

I'll get you started.

Step 1: Thief #1

There are x breads, and if thief #1 takes half of these plus one-half of one, then the expression that represents the number of breads that remain after this first action is\[x -(\frac{ 1 }{ 2 }x +\frac{ 1 }{ 2 })=\frac{ 1 }{ 2 }x -\frac{ 1 }{ 2 }\]Understood?!

Answer 23

Very Good! @nitz

Answer 24

now, what's next? as for the second: x/4-3/4

Answer 25

@irene22988 I'm trying to teach. Please stop giving out answers right now!

Answer 26

O.o

Answer 27

I'm going to report anyone who gives out anymore answers, UNDERSTOOD?!

Answer 28

i am just wondering: are we going to solve this by individually evaluating the number of remaining bread per thief?

Answer 29

my bad. sorry.

Answer 30

Step 2: Thief #2
Now there are\[\frac{ 1 }{ 2 }x -\frac{ 1 }{ 2 }\]breads remaining. Thus thief #2 now starts with these many breads. If he takes half of these plus one-half of one bread, then he takes\[\frac{ 1 }{ 2 }(\frac{ 1 }{ 2 }x -\frac{ 1 }{ 2 })=\frac{ 1 }{ 4 }x +\frac{ 1 }{ 4 }\]Now the expression that represents the number of breads that remain after this second action is\[(\frac{ 1 }{ 2 }x -\frac{ 1 }{ 2 })-(\frac{ 1 }{ 4 }x +\frac{ 1 }{ 4 })=\frac{ 1 }{ 4 }x -\frac{ 3 }{ 4 }\]

Answer 31

Are we understanding thus far? If so then please humour me. Describe step 3: Thief #3, and thus tell me what is the expression that represents the number of breads that remain after this third action.

Answer 32

Hahahahaha

Answer 33

I never said that @Algebraic! Why don't you wait 'til the end, and if I get it wrong (which guaranteed I won't), then you may get the satisfaction of criticizing me. Deal?

Answer 34

I'm not talking about a quarter of a bread, I'm talking about an expression.

Answer 35

use the partial sum of a series.

Answer 36

come on let him do what he is doing

Answer 37

@Algebraic! clearly they are not at that level, besides I didn't see you jumping in at the beginning. It's always very easy to be critical of others.

Answer 38

Thank you @Fazeelayaz

Answer 39

So do you know the expression that represents the number of breads that remain after this third action? That was my question to you before @Algebraic! rudely interrupted, while offering no real value.

Answer 40

@Fazeelayaz do you know the expression that represents the number of breads that remain after this third action or not?

Answer 41

(x/4-3/4)-(x/8-3/8)=x/8-3/8

Answer 42

Almost but not quite! You inadvertently forgot to add one-half of a loaf to the expression for the number of loaves of bread the third thief takes. Care to give it another try @Fazeelayaz

Answer 43

well i don't understand

Answer 44

That's alright! Allow me to explain. The second thief had left behind\[\frac{ 1 }{ 4 }x -\frac{ 3 }{ 4 }\]breads behind. Now the third thief takes half of these loaves of bread plus one-half of a loaf.Thus the third thief takes\[\frac{ 1 }{ 2 }(\frac{ 1 }{ 4 }x -\frac{ 3 }{ 4 })+\frac{ 1 }{ 2 }=\frac{ 1 }{ 8 }x +\frac{ 1 }{ 8 }\]Correct? Now the expression that represents the number of breads that remain after this third action is what? @Fazeelayaz ?

Answer 45

x/4-3/4-(x/8+1/8)=x/8-7/8

Answer 46

Excellent!! @Fazeelayaz Do you now see what error you made earlier?

Answer 47

yes

Answer 48

Great! @Fazeelayaz Now similarly can you tell me the expression that represents the number of loaves of bread that remain after the fourth action? Hence Step 4: Thief #4?

Answer 49

x/16-7/16+1/2=x/16+1/16

x/8+1/8-(x/16+1/16)=x/16+1/16

Answer 50

@Fazeelayaz that's the expression for the number of loaves of bread that thief #4 takes. What is the expression that represents the number of loaves of bread that remain after this fourth action?

Answer 51

same

Answer 52

No @Fazeelayaz please try again.

Answer 53

x/16-7/16+1/2=x/16+1/16


x/8-7/8-(x/16+1/16)=x/16-15/16

Answer 54

Correct!! Very Good! Now can you tell me the expression that represents the number of loaves of bread that remain after the fifth action?

Answer 55

x/32-15/32+1/2=x/32+1/32


x/16-15/16-(x/32+1/32)=x/32-31/32

Answer 56

@Fazeelayaz YES!! Now after this fifth action, there were 3 breads left, thus equate this final expression to 3, and solve for x. Go ahead @Fazeelayaz

Answer 57

x/32-31/32=3
x-31=96
x=96+31
x=127

Answer 58

PERFECT!!! SEE, YES YOU CAN!! EXCELLENT!!!

∴ there were initially 127 loaves of bread!

Answer 59

thank u very much

Answer 60

o thanks for that too

Answer 61

well i have to go iam extremelly hungry THANKS FOR UR TIME SIR

Answer 62

Im glad dat @Fazeelayaz got it... Cheer up Hip hip HOOORAY =D =D

Answer 63

You're very welcome, we could have finished this way before if others hadn't been obnoxious and kept rudely interrupting but that's okay. What matters most is that you @Fazeelayaz , @nitz , and @Algebraic! learned how to properly solve these types of problems. Excellent work @Fazeelayaz !!!!!!!

Answer 64

@Fazeelayaz is there anything else I can help you with?

Answer 65

Well done @calculusfunctions u taught alot of people..SHOWERS OF BLESSINGS =D

Answer 66

Thank you @Ivanka123

Answer 67

Ur most welcome =D