SOLUTION: . A sheep fold was robbed 3 nights successively. The first night one half were stolen and half a sheep more. The second night half the remainder were lost and half a sheep more, th

Question 983149: . A sheep fold was robbed 3 nights successively. The first night one half were stolen and half a sheep more. The second night half the remainder were lost and half a sheep more, the last night they took half that were left and half a sheep more, by which time they were reduced to 20. How many were there at first ?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A sheep fold was robbed 3 nights successively. The first night one half were stolen and half a sheep more. The second night half the remainder were lost and half a sheep more, the last night they took half that were left and half a sheep more, by which time they were reduced to 20. How many were there at first ?
:
Let x = original number of sheep
:
After 1st night robbery (how do you steal half a sheep?)
x - (.5x + .5)
x - .5x - .5
.5x - .5 remain
After 2nd night robbery
.5x - .5 - .5(.5x + .5)
.5x - .5 - .25x - .25
.25x - .75 remain
After the 3rd night
.25x -.75 - .5(.25x-.5) = 20
.25x - .75 - .125x - .25 = 20
.125x - 1 = 20
.125x = 20 + 1
.125x = 21
x = 21/.125
168 sheep originally
:

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

. A sheep fold was robbed 3 nights successively. The first night one half were stolen and half a sheep more. The second night half the remainder were lost and half a sheep more, the last night they took half that were left and half a sheep more, by which time they were reduced to 20. How many were there at first ?

Original number:
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