Math Count - St Patrick's Day Math

Problem:
Last Thursday, March 17 was St. Patrick’s Day when, typically, more people than usual wear some article of green clothing. Patrick has a leprechaun hat that looks like a tall, green top hat. The main portion of the hat is a cylinder that is 8 inches tall and has a 3-inch radius. He filled this portion of the hat with chocolates wrapped to resemble small gold coins to pass out to all his friends. One bag of these chocolate “coins” takes up about 20 in cubed of space. What is the minimum number of bags of chocolate that Patrick must get to completely fill his hat?

Margaret painted a mural for St. Patrick’s Day and mixed her own green paint. She mixed 3 parts yellow paint with 2 parts blue paint to create green paint. Maureen wanted to also paint a mural with the same green color, but she currently has 8 cups of green paint that is a mixture of 40% yellow paint and 60% blue paint. To get the same shade of green as Margaret, how many cups of yellow paint must she add to her mixture?

Let’s now take a look at the word GREEN. There are not too many real words that can be made from the letters in GREEN. For this problem, though, let’s see how many ways we can arrange the five letters in the word GREEN, even if they don’t form real words. But let’s also add a restriction: any arrangement must keep the two Es together. How many such arrangements are there?

Key 1: Sketch the cylinder
Key 2: Equivalent ratios
Key 3: Permutation formula

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