Answer :
I used a matrix equation to solve this, but I got decimal answers. I may have done something wrong, but here is what I got.
Rita has 32 nickels, 21&1/3 dimes, and 42&2/3 quarters.
Robin would have 17 nickels, 27 dimes, and 54 quarters.
Rita has 32 nickels, 21&1/3 dimes, and 42&2/3 quarters.
Robin would have 17 nickels, 27 dimes, and 54 quarters.