Let's name #a# the number of dimes and #b# the number of quarters.

A dime is $0.1 and a quarter is $0.25

Thus : #0.1a+0.25b=4.5#

And we know that she has 3 more dimes than quarters

Thus : #a=b+3#

We just replace the value of a in the equation :

#0.1*(b+3)+0.25b=4.5#

#0.1b+0.3+0.25b=4.5#

#0.1b+0.25b=4.5-0.3# ( we substract 0.3 on each side )

#0.35b=4.2#

#b=4.2/0.35# ( we divide by 0.35 on each side )

#b=12# : Laura has #12# quarters

We can now get #a# :

#0.1a+0.25b=4.5#

#0.1a+0.25*12=4.5#

#0.1a+3=4.5#

#0.1a=4.5-3# ( we substract 3 on each side )

#0.1a=1.5#

#a=1.5/0.1# ( we divide by 0.1 on each side )

#a=15# : Laura has #15# dimes

We can now verify :

#15*0.1+12*0.25=1.5+3=4.5# : correct !

And #15=12+3#, so Laura has #3# more dimes than quarters : perfect