Final answer:
The weight of the cheese that contains 112 calories is 28 grams. This is calculated using direct variation, with the provided information that 200 calories correspond to 50 grams of cheese.
Step-by-step explanation:
To answer the question about how much cheese weighs if it has 112 calories, we need to use the concept of direct variation. This concept tells us that the number of calories in cheese varies directly as the weight of the cheese. We are given that there are 200 calories in 50 grams of cheese, which allows us to set up the following proportion to solve for the weight of the cheese with 112 calories:
200 calories (kcal) / 50 grams = 112 calories (kcal) / w grams
Cross-multiplying gives us:
200 * w = 112 * 50
Dividing both sides by 200 to find w gives us:
w = (112 * 50) / 200
Therefore, the weight of the cheese that contains 112 calories is calculated as follows:
w = 5600 / 200
w = 28 grams
So, if the cheese has 112 calories, it weighs 28 grams.