A man is mixing sugar and water for his bird feeder. He uses 1/3 of a teaspoon of sugar for 1/2 cup of water. what is the unit rate of sugar per cup of water? how much sugar will he need to mix into 12 cups of water? Show your work
To find the unit rate of sugar per cup of water, we can set up a proportion:
1/3 teaspoon of sugar / 1/2 cup of water = x teaspoon of sugar / 1 cup of water
To cross multiply, we get:
1/3 * 1 = x * 1/2
x = 1/6 teaspoon of sugar per cup of water
To find how much sugar he will need to mix into 12 cups of water, we can set up another proportion:
1/6 teaspoon of sugar / 1 cup of water = x teaspoon of sugar / 12 cups of water
To cross multiply, we get:
1/6 * 12 = x * 1
x = 2 teaspoons of sugar
Therefore, he will need to mix 2 teaspoons of sugar into 12 cups of water.