Question 1210636
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Let x be the "inside" length in inches of each link.<br>
Since the thickness of the links is .5 inches, the length of a "chain" of 1 link is (x+1) inches.<br>
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.<br>
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.<br>
Since the longer chain is 14 inches longer than the shorter chain...<br>
6x = 14
x = 14/6 = 7/3<br>
The length of the shorter chain is 22 inches.  To find the number of links in that chain...<br>
nx+1 = 22
n(7/3)+1 = 22
(7/3)n = 21
n = 21/(7/3) = 9<br>
ANSWERS: The number of links in the shorter chain is 9; the number in the longer chain is 9+6 = 15<br>