Here you go:
Set the number of nickels as “n”, the number of dimes as “d”, and the number of quarters as “q”.
There are a total of 37 coins. Therefore:
n+d+q=37
You also know that the total in dollar amounts is equal to $5.50. Therefore:
.05n+.10d+.25q=5.50
In the first equation, we can set q = n+4 (as there are 4 more quarters than nickels). Resetting the first equation:
n+(n+4)+d=37
Solve for “d” in terms of “n”:
d=33-2n
Now we set the second equation (using q=n+4):
.05n+.10d+.25(n+4)=5.50
Now you can plug the “d=33-2n” value to the above equation to solve for “n”:
.05n+.10(33-2n)+.25(n+4)=5.50
Do all the annoying math, and the final answer is n=12. That gives you the number of nickels. Finally:
#n=12
#q=16
#d=37-28=9
and that’s your answer! Double check your work and make sure the math is right:
.05(12)+.1(9)+.25(16)=5.5
Hope that answers your question! Just keep in mind the moral of the equation: if you have multiple variables (like you do here), you need to set up equations to solve for a variable in terms of a main variable – which in this case I made “n” as our main variable.