Final answer:
To find out how much drink mix is needed for 5 cups of water, you use proportional reasoning. Given the ratio of 2 cups of water to 1/2 teaspoon of mix, 1 cup of water would require 1/4 teaspoon of mix. Therefore, 5 cups of water would require 1.25 teaspoons of mix.
Step-by-step explanation:
The question is asking how much drink mix is needed if you have 5 cups of water, given that the ratio of water to drink mix is 2 cups to 1/2 teaspoon. To solve this, you need to use proportional reasoning.
First, note that 1/2 teaspoon of mix is used for 2 cups of water. This is a ratio of 1/2 teaspoon to 2 cups. Thus, 1 cup of water would require (1/2) / 2 = 1/4 teaspoon of mix. This is your unit rate or proportion metric.
Now, if you have 5 cups of water, you multiply this by the unit rate to find out how much drink mix you need: 5 * 1/4 = 5/4 = 1.25 teaspoons of mix. So, you would need 1.25 teaspoons of mix for 5 cups of water.
Learn more about Proportional Reasoning