Final answer:
The correct equation representing the relationship between the number of batches of cookies (c) and the number of cups of sugar (s) is c = (2/3) × s, maintaining the proportion of the recipe. Therefore, the correct option that represents the relationship between c and s is: c = (2/3) ( times) s
Step-by-step explanation:
When Emily makes 6 batches of cookies, she uses 4 cups of sugar. Following this recipe, the ratio of cups of sugar to batches of cookies is 4 cups of sugar per 6 batches, which simplifies to 2/3 cup of sugar per 1 batch of cookies. Now, if Michael wants to make c batches of cookies, he'll need to maintain the same ratio. Using a simple proportion, we can relate the quantities of batches (c) and cups of sugar (s) as follows: 4 cups / 6 batches = s cups / c batches. Multiplying both sides of the equation by c batches we get 4/6 ( times ) c = s. Simplifying 4/6, we get 2/3, so the relationship is 2/3 ( times ) c = s.
Therefore, the correct option that represents the relationship between c and s is:
c = (2/3) ( times) s