The other day, we made drink mixtures by mixing 4 teaspoons of powdered drink mix for every cup of water. Here are two ways to represent multiple batches of this recipe: How can we tell that 4:1 and 12:3 are equivalent ratios?

How are these representations the same? How are these representations different?

How many teaspoons of drink mix should be used with 3 cups of water?
How many cups of water should be used with 16 teaspoons of drink mix?
What numbers should go in the empty boxes on the double number line diagram? What do these numbers mean?