A good way to think about it is backwards. They paid 20: 20is the goal. They paid 17.75. So resolve the awkward coins first. Hit them with a .25 to make 18. Now, hit them with 1s until you make 20. So add 2.
Until you hit amounts greater than 30, they will always pay to the nearest divisible by 5, so you can usually just add coins, from smallest (minus pennies) to largest, until their subtotal reaches the nearest divisible by 5 number. Though this thought process did screw me over when they paid 32 on a 40...