1 nickel = 5 cents

1 dime = 10 cents

Let

n = the number of nickels, n>=0, n is integer

d = the number of dimes, d>=0, d is integer

Ashley has 15 coins altogether:

n + d = 15

The total value of the coins is $1.25 = 125 cents:

5n + 10d = 125

We have the following system of equations:

n + d = 15

5n + 10d = 125

........

click here to see the system of equations solved for d and n

........

d = 10 dimes

n = 5 nickles

John has 5 nickles and 10 dimes.