1 nickle = 5 cents

1 quarter = 25 cents

let

n = the number of nickels

q = the number of quarters

you have 15 coins in your pocket that are either quarters or nickles

n + q = 15

they total $2.75 = 275 cents

5n + 25q = 275 divide both sides by 5

n + 5q = 55

by solving the system of equations

n + 5q = 55

n + q = 15

we find

n = 5 nickels

q = 10 quarters

click here to see the step by step solution of the system of equations

I have 5 nickles and 10 quarters.