SOLUTION: *The sum of 5% of one number and 4% of a second number is 44. The sum of 4% of the first number and 5% of the second number is 46. Find the numbers.

0.05*x + 0.04*y = 44,    (1)
0.04*x + 0.05*y = 46.    (2)

Multiply everything by 100. You will get

5*x + 4*y = 4400,       (1')
4*x + 5*y = 4600.       (2')

Add (1') and (2') and divide by 9. You will get

x + y = 1000.           (3)

Distract (2') from (1'). You will get

x - y = -200.           (4)

Next, add (3) and (4) to get 2x = 1200,  x = 600.

Now from (3) y = 1000 - 600 = 400.

Let 1st number be F, and 2nd, S

We then get: .05F + .04S = 44 ------- eq (i)

Also,        .04F + .05S = 46 ------- eq (ii)

              .2F + .16S = 176 ------ Multiplying eq (i) by 4 ------- eq (iii)

            - .2F - .25S = - 230 ---- Multiplying eq (ii) by - 5 ---- eq (iv)

                  - .09S = - 54 ----- Adding eqs (iii) & (iv)

        S, or 2nd number = , or 

         .04F + .05(600) = 46 ------- Substituting 600 for S in eq (ii)

               .04F + 30 = 46

                    .04F = 46 - 30

                    .04F = 16

        F, or 1st number = , or