SOLUTION: Cycle Center has bicycles and tricycles in the storeroom. There are at least three of each, and there are more bicycles than tricycles. There are 28 wheels altogether. How many bic

b = number of bicycles
t = number of tricycles

2b + 3t = 28

2 is the smaller coefficient in absolute value. So write each number 
which is not a multiple of 2 in terms of its nearest multiple of 2.

So we only need to write the 3 as 2+1

2b + (2+1)t = 28
2b + 2t + t = 28

Divide each term by 2

 b + t + t/2 = 14

Isolate any fractions

         t/2 = 14 - b - t

The right side is an integer, so the left side must be equal to the
same integer.  Let that integer be K

t/2 = K,    14 - b - t = K

  t = 2K,   14 - b - 2K = K

                14 - 3K = b

      b > t
14 - 3K > 2K
     14 > 5K
    2.8 > K
      K ≤ 2 since K is an integer

 
t = 2K ≥ 3,   b = 14 - 3K ≥ 3
     K ≥ 1.5,         -3K ≥ -14
     K ≥ 2              K ≤ 14/3
                        K ≤ 4.333...
                        K ≤ 4
(since K is an integer)

Since K ≤ 2 and K ≥ 2, then K = 2

Thus t = 2K = 2(2) = 4 tricycles and
     b = 14 - 3K = 14 - 3(2) = 14-6 = 8 bicycles.

Edwin