Coin Stacks II

It is possible to mix coins in a stack to get a stack a whole number of millimeters high. For example, a stack of 2 nickels and 2 pennies has a height of exactly 2 × 1.95 + 2 × 1.55 = 7 mm. Can you find a stack of coins with a whole number of millimeters less than 7?

Coin Stacks

US coins have different thicknesses as specified below:

Penny	1.55 mm
Nickel	1.95 mm
Dime	1.35 mm
Quarter	1.75 mm

Two stacks of coins may have the same height but a different number of coins. For example, a stack of 39 pennies has a height of 39 × 1.55 = 60.45 mm, and a stack of 31 nickels also has a height of 31 × 1.95 = 60.45 mm. Find the smallest number of dimes and quarters that can likewise be made into two stacks the same height.

Paying Bills

Rosa pays bills from her checking account. Her balance before paying bills is $632.74. She pays her energy bill for $237.29 and her water bill for $47.93. She also pays her telephone bill for $33.72. What is Rosa's checking balance after paying her bills?

Paper Weight

A ream of bond paper consists of 500 sheets each 11" x 17". The weight of the paper refers to how much a ream weighs. For example, 24# paper weighs 24 pounds by the ream and is thicker and heavier than 20# paper. What is the nominal weight of a single sheet of 24# letter size (8.5" x 11") paper? Express your answer in ounces with 3 significant digits.