Question 1183260: Hi
A breeder sold half of his horses,then sold another 2. He then sold of his remaining horses then another 2. He then had 1 horse left. How many did he have at first.
Thanks.
Found 2 solutions by ankor@dixie-net.com, ikleyn:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A breeder sold half of his horses, then sold another 2.
He then sold half of his remaining horses then another 2.
He then had 1 horse left.
How many did he have at first
:
let x = no. of horses originally
"A breeder sold half of his horses, then sold another 2."
x - (.5x+2) = .5x-2 left
"He then sold HALF of his remaining horses then another 2." (Edited to make sense)
"He then had 1 horse left"
.5x-2 - (.5(.5x-2) + 2) = 1
.5x -2 - (.25x - 1 + 2) = 1
.5x - 2 - .25x + 1 - 2 = 1
.5x - .25x - 2 - 1 = 1
.25x - 3 = 1
.25x = 3 + 1
.25x = 4
x = 4 * 4
x = 16 horses
Answer by ikleyn(52814)  (Show Source):
You can put this solution on YOUR website! .
A breeder sold half of his horses, then sold another 2.
He then sold of his remaining horses then another 2.
He then had 1 horse left. How many did he have at first.
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This entertainment problem can be solved mentally, without using equations.
The method of solving such problems mentally is to go back from the end to the beginning.
In order to better represent the selling process, I will reformulate the problem.
Step 1. Sold the half of the horses.
Step 2. Sold another 2 horses.
Step 3. Sold the half of remaining horses.
Step 4. Sold another 2 horses.
Step 5. Had 1 horse left.
Now I will move from the end to the beginning.
(a) Before step 4, he had 1+2 = 3 horses.
(b) This 3 horses are half of what he had before step 3.
Hence, before step 3, he had 2*3 = 6 horses.
(c) Before step 2, he had 6+2 = 8 horses
(d) These 8 horses are the half of what he had before step 1.
Hence, initially, the breeder had 2*8 = 16 horses.
ANSWER. Initially, the breeder had 16 horses.
Solved.
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This problem and this method of solution is good to teach very young children (from kindergarten to the 2nd, 3rd or 4th grade).
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