Final answer:
To find the amount of water in 100 ounces of grapefruit juice, you set up a proportion using the given 12-ounce serving as a reference. By solving the proportion, it's determined that 100 ounces of grapefruit juice contains 1250 grams of water. The correct option is A.
Step-by-step explanation:
Proportion and unit conversion are the key mathematical concepts involved in solving this problem regarding the amount of water in grapefruit juice when scaling up from a 12-ounce serving to a 100-ounce quantity.
To determine the amount of water in 100 ounces of grapefruit juice, we first establish the ratio of water to juice based on the given 12-ounce serving. Since a 12-ounce serving contains 150 grams of water, we then use a unit conversion factor to calculate the amount of water for the desired 100-ounce serving. The conversion factor here is based on the relationship 1 oz = 28.349 g.
To find the answer, we set up a proportion: (150 g water / 12 oz juice) = (X g water / 100 oz juice). Solving for X gives us the amount of water in 100 ounces of grapefruit juice. Multiplying both sides of the equation by 100 and then dividing by 12 gives us X = 150 g × 100 oz / 12 oz, which simplifies to X = 1250 grams of water.