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**aznmartinjai** The seats ‘R’ Us factory produces chairs with four legs and stools with three legs. The style of seats and legs are all the same. This year, if all the leftover legs were put with the leftover seats to make chairs, one seat would be left over without any legs. However, if all the leftover legs were put on the leftover seats to make stools, one leg would be left. How many more legs than seats are in the leftover inventory?

Hello,

let l be the number of legs

let c be the number of seats

let s be the number of stools

then you get the equations.

4(c-1) = l

3s + 1 = l

Eliminate l:

4c - 4 = 3s + 1 ===> c = (3/4)s + (5/4) = (1/4)(3s + 5)

c must be an integer; therefore you are looking for a value of s so that (3s+5) is a multiple of 4. The first possible value is s = 1 then c = 2 and you had 4 legs left over.

Make a table to see the pattern behind this problem: Code:

c s l
--------------------------
2 1 4
5 5 16
8 9 28
11 13 40
: : :
: : :
2+3n 1+4n 4+12n

EB