Let x = be the number of dimes and y = number of quarters.
Since the total number of coins is 100, x + y = 100.
Since the total is cent value is 19.75, comprised of .10 for dimes and .25 for quarters, we have .10x + .25y = 19.75.
This is just a system of equations. Solve one of the dozen ways that work for solving systems of linear equations.
Using substitution:
x = 100 - y
Plug this into the other equation
.10 (100 - y) + .25 y = 19.75
10 - .10 y + .25 y = 19.75
10 + .15y = 19.75
.15 y = 9.75
y = 65
So there are 65 quarters. Since x + y = 100, there must be 35 dimes.Hope This Helps
