Joe has a collection of nickels and dimes that is worth $5.30. If the number of dimes was tripled and the number of nickels was increased by 14, the value of the coins would be $14.90. How many nickels and dimes does he have?

Suppose n represents the number of nickels and d represents the number of dimes. The conditions of the problem can be written as
  .10d + .05n = 5.30
  .10*(3d) + .05*(n+14) = 14.90
Multiplying the first equation by 3 and subtracting the second gives
  3(.10d + .05n) - (.10*(3d) + .05*(n+14)) = 3(5.30) - (14.90)
  .05*(3n - (n+14)) = 1.00
  2n - 14 = 20.  (divide by .05)
  2n = 34
  n = 17
  d = (5.30 - .05*17)/.10 = 44.5
I have worked this problem another way (offline) and got the same result. There is no solution that gives an integer number of dimes.