1 quarter = 25 cents

1 nickle = 5 cents

let

q = the number of quarters Doming picks up, q is integer, q >= 0

n = the number of nickles Domingo picks up, n is integer, n >= 0

Domingo picks up 5 coins from his collection of quarters and nickels:

q + n = 5

lets assume he picks up exactly $0.50 = 50 cents. in that case we have:

25q + 5n = 50 divide both sides by 5

5q + n = 10

by solving the system of equations:

q + n = 5

5q + n = 10

we find:

q = 3.75

n = 1.25

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

since the solutions are not integers (there are no integer solutions of the system) follows Domingo can not pick up exactly $0.50.