Let:
x= quarters
y= dimes
x+y=67
and
.25x+.10y=12.40
x=67-y
.25(67-y)+.10y=12.40
16.75-.25y+10y=12.40
16.75-.15y=12.40
Lets rearrange this:
-.15y+16.75=12.40
-16.75 -16.75
-.15y=-4.35
the negatives cancel out
.15y=4.35
.15 .15
y=29
Back to the original x=67-y
x=67-29
x=38
So,
x=38
y=29
