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
