How to write regina has 120 coins, all quarters and dimes. she has 10 more dimes than quarters. how many quarters and dimes does she have as an equation

So Regina has 120 coins=total
120=total
we will use q=number of quarters and d=number of dimes
120=d+q
she has 10 more dimes than quarters
d=q+10
so if we susitute this into the equation then we get
120=(q+10)+q
add  like terms
120=2q+10
subtract 10 from both sides
110=2q
divide both sides by 2
55=q
she has 55 quarters
subtitute into second equation
d=10+55
d=65

dimes=65
quarters=55

Iam pretty sure its a sorry if im wrong