Maria has a total of 95 dimes and quarters. if the total value of the coins is $23.45, how many quarters does she have? show work.

This is the concept of application of quadratic equations; To get the number of dimes and quarters we proceed as follows;
suppose there are x dimes and y quarters;
x+y=95i
but we know;
$0.1=1 dimes
$0.25=1 quarters 
thus
0.1x+0.25y=23.45ii
solving equation i and ii by substitution we shall have:
from i;
x=95-y
thus substituting the value of x in equation ii we get
0.1(95-y)+0.25y=23.45
9.5-0.1y+0.25y=23.45

collecting like terms we get:
0.15y=13.95
dividing both sides by 0.15 we get;
y=13.95/0.15=93
x=95-93=2
therefore we conclude that there were 2 dimes and 93 quarters