Giuliana has 22 quarters and dollar coins worth a total of $10.75

Quarter is $0.25

Dollar is just $1

x is amount of quarters

y is amount of dollar coins

Two equations we know

0.25x+1y=10.75 and

x+y=22

solve both for y

0.25x+1y=10.75

y=10.75-0.25x

x+y=22

y=22-x

set them equal

22-x = (y) = 10.75-0.25x

11.25=0.75x

x=15 quarters

then put x=15 into either equation and now solve for y

x+y=22

15+y=22

y=7 dollar coins