Lizzy: There are 28 garden gnomes in a yard. Three-fourths of them have red hats, and the rest have blue hats. Half the garden gnomes have big noses instead of small noses. If six gnomes with blue hats have big noses, how many gnomes with red hats have small noses?.
Me: Hmmm, let me think. I think this is the detailed solution:
Half the gnomes have big noses, so 28 / 2 = 14 have big noses. Three - quarters of the gnomes have red hats, so 28 * 3 / 4 = 21 gnomes have red hats. There are 6 gnomes with blue hats and big noses, so there are 14 - 6 = 8 with red hats and big noses. Thus, there are 21 - 8 = 13 gnomes with red hats that have small noses. Final answer: 13.