SOLUTION: An electric company is placing utility poles along a road. It is determined that 5 fewer poles per kilometre would be necessary if the distance between the poles were increased by

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Question 132098: An electric company is placing utility poles along a road. It is determined that 5 fewer poles per kilometre would be necessary if the distance between the poles were increased by 10metres. How many poles are being placed each km?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
n= number of poles in a km
x+= initial distance between poles in meters
(1) n+=+%281000%2Fx%29+%2B+1 add 1 to account for poles at start and finish
(2) n+-+5+=+1000%2F%28x%2B10%29+%2B+1
Add 5 to both sides of (2)
n+=+1000%2F%28x%2B10%29+%2B+6
Set the right side equal to right side of (1)
1000%2F%28x%2B10%29+%2B+6+=+1000%2Fx+%2B+1
multiply both sides by x%2A%28x%2B10%29
1000x+%2B+6x%2A%28x%2B10%29+=+1000%2A%28x%2B10%29+%2B+x%2A%28x%2B10%29
1000x+%2B+6x%5E2+%2B+60x+=+1000x+%2B+10000+%2B+x%5E2+%2B+10x
5x%5E2+%2B+50x+-+10000+=+0
divide through by 5
x%5E2+%2B+10x+-+2000+=+0
complete the square
x%5E2+%2B+10x+%2B+%2810%2F2%29%5E2+=+2000+%2B+%2810%2F2%29%5E2
%28x+%2B+5%29%5E2+=+2025
x+=+45+-+5
x+=+40 m between poles
check answer:
(1) n+=+%281000%2Fx%29+%2B+1
(2) n+-+5+=+1000%2F%28x%2B10%29+%2B+1
---------------------------------
(1) n+=+%281000%2F40%29+%2B+1
n+=+26
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(2) n+-+5+=+1000%2F%2840%2B10%29+%2B+1
n+-+5+=+21
n+=+26
OK