let

x = the number of dimes, x is positive integer

y = the number of quarters, y is positive integer

1 dime = 10 cents

1 quarter = 25 cents

10x + 25y = 95 divide both sides by 5

2x + 5y = 19

x = (19 - 5y)/2 =>

19 - 5y is even number and that is possible if and only if y is odd (if y is even then 19 - 5y will be odd)

19 - 5y >0

y < 19/5 < 5

y < 5

we have the following possibilities

y = 1 => x = 7

Luis has 7 dimes and 1 quarter.

y = 3 => x = 2

Luis has 2 dimes and 3 quarters.