It is often easy to work these problems if you can arrange the coins in equal groups. In cases where there are a few more or less of one than another, you can add or subtract the appropriate number of coins to make it come out even.
4. Subtracting 3 quarters ($0.75) Rudolph will have $6.50 and an equal number of nickels and quarters with twice as many dimes. That is, Rudolph can group his coins into groups consisting of 1 quarter, 1 nickel, and 2 dimes, for a total of $.50 per group. 6.50/0.50 = 13 groups will make up the revised total.
Rudolph has 13 nickels, 26 dimes, and 16 quarters.
5. Adding 2 dimes to the total will allow Andrea to group her coins into groups that have 1 quarter, 4 nickels, and 4 dimes. Each group is worth $0.85, and her revised total will be $2.55. That is, she has 2.55/0.85 = 3 groups of coins.
Andrea has 3 quarters, 12 nickels, and 10 dimes.