Question 1210636: 2 portions of metal chain has the following description:
Circular links, all same size, .5 inches in thickness.
Chain A: 3 feet in length.
Chain B: 22 inches in length.
One portion contained 6 links more than the other.
Calculate number of links in each chain.
Not sure how to solve.
Answer by greenestamps(13367)   (Show Source):
You can put this solution on YOUR website!
Let x be the "inside" length in inches of each link.
Since the thickness of the links is .5 inches, the length of a "chain" of 1 link is (x+1) inches.
Adding each new link increases the total length of the chain by x inches, so the length of a chain of 2 links is (2x+1) inches, the length of a chain of 3 links is (3x+1) inches,... and the length of a chain of n links is (nx+1) inches.
The longer chain in the problem contains 6 more links than the shorter chain, so the difference in the lengths of the two chains is 6x.
Since the longer chain is 14 inches longer than the shorter chain...
6x = 14
x = 14/6 = 7/3
The length of the shorter chain is 22 inches. To find the number of links in that chain...
nx+1 = 22
n(7/3)+1 = 22
(7/3)n = 21
n = 21/(7/3) = 9
ANSWERS: The number of links in the shorter chain is 9; the number in the longer chain is 9+6 = 15
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