Math problem help

Question

Kelly has a collection of nickels, dimes and quarters with a total value of $10.45$10.45. There are 77 more dimes than nickels and 22 times more quarters than nickels, how many of each coin does she have?

Answer 1

5N+10D+25Q = 1045

D=77+N

Q=22N

Zero Nickels

77 Dimes

11 Quarters

5(0) + 10(77) + 25(11) = 1045

but then Q doesn't = 22 times 0

There's a mistake in the problem somewhere

as written the only solution is about slightly less than 1/2 a Nickel, about 0.486726 Nickels

Dimes = about 77.486726

and Quarters = about 22 times .486726 = 10.708

round them off to nearest integer gives N=0, D=77, Q=11