Teresa has $4.50 worth of change in nickels and dimes if she has 4 times as many nickels as dimes how many of each type of coin does she have
Let x be the number of dimes.
Teresa has 4*x = 4x nickels.
The value of the dimes is 10*x cents.
The value of the nickels is 5*4x = 20x cents.
The total value of the coins is 10x + 20x = 450 cents.
This simplifies to 30x = 450.
Thus, the number of dimes is x = 450/30 = <<450/30=15>>15.
And the number of nickels is 4*15 = <<4*15=60>>60. Answer: \boxed{15, 60}.