A gnome is wearing 1 hat and 2 boots.

If you had 66 boots and hats combined, how many gnomes would you have?
GNOMES: 1, 10, 20, 21, 22
BOOTS: 2, 20, 40, 42, 44
HATS: 1, 10, 20, 21, 22
TOTAL: 3, 30, 60, 63, 66

1 answer

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.