Let x=number of nickels
Then x+4=number of quarters
So the number of dimes would be:
37-x-(x+4)=
37-2x-4=
33-2x —- is the number of dimes
(lets deal in pennies)
5x+25(x+4)+10(33-2x)=550
so 5x+25x+100+330-20x=550
collect like terms
10x+430=550
subtract 430 from each side
10x+430-430=550-430=
10x=120
divide each side by 10
x=12
number of nickels
x+4=12+4=16
number of quarters
33-2x=33-24=9
number of dimes
Check
5*12=60
25*16=400
9*10=90
60+400+90=550
550=550