To determine how many gnomes you could have with a combined total of 66 boots and hats, let's set up the relationship based on what a single gnome has.
Each gnome has:
- 1 hat
- 2 boots
This means for each gnome:
- The total number of hats contributed by gnomes will be equal to the number of gnomes (let's call the number of gnomes \( G \)).
- The total number of boots contributed by gnomes will be \( 2G \).
The equation for the total number of hats and boots combined is: \[ G + 2G = 3G \]
Given that the total number of hats and boots combined is 66, we can set the equation: \[ 3G = 66 \]
To find \( G \): \[ G = \frac{66}{3} = 22 \]
Thus, the number of gnomes would be 22.