A cafeteria has created a healthy snack by mixing unsalted cashews and peanuts in a ratio of 2:3 respectively. If Jane has 4 pounds of cashews, how many pounds of peanuts does she have to use?
Jane has to use 6 pounds of peanuts.
To maintain the 2:3 ratio of cashews to peanuts, if Jane has 4 pounds of cashews, she must calculate the corresponding amount of peanuts based on this ratio. The ratio indicates that for every 2 parts of cashews, there are 3 parts of peanuts, leading to a necessary calculation to find the exact weight of peanuts needed.
Using only 4 pounds of peanuts would not satisfy the 2:3 ratio, as this would imply a ratio of 1:1 with the 4 pounds of cashews. This is incorrect because it does not account for the required proportion of peanuts needed in relation to the cashews.
This is the correct answer. Given the ratio of 2:3, if Jane has 4 pounds of cashews (representing 2 parts), then the corresponding amount of peanuts (3 parts) can be calculated using the proportion: (3 parts/2 parts) × 4 pounds = 6 pounds. This maintains the necessary ratio.
Using 8 pounds of peanuts would create a ratio of 2:4 when compared to the 4 pounds of cashews, thus simplifying to 1:2. This does not satisfy the original ratio of 2:3 and demonstrates an incorrect calculation based on the relationship defined in the problem.
10 pounds of peanuts significantly exceeds the required amount according to the 2:3 ratio. This would create an even greater discrepancy in the ratio, leading to a misalignment with the 4 pounds of cashews and thus would not be a valid solution.
To achieve the desired ratio of 2:3 between cashews and peanuts, Jane must use 6 pounds of peanuts when she has 4 pounds of cashews. This calculation ensures that the proportions are maintained correctly, aligning with the healthy snack creation in the cafeteria. Miscalculating the ratio leads to incorrect amounts that do not meet the specified criteria.
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