Final answer:
To determine the number of peanuts needed for 1 cup of raisins in a trail mix recipe, you can use the ratio provided in the question. For every 3 cups of raisins, 1/2 cup of peanuts is needed. By multiplying both sides of the ratio by 2, you can find that 6 cups of raisins require 1 cup of peanuts. Therefore, for 1 cup of raisins, you will need 1/6 cup of peanuts.
Step-by-step explanation:
To determine the number of peanuts needed for 1 cup of raisins, we first need to find the ratio of raisins to peanuts in the trail mix recipe. The recipe calls for 3 cups of raisins for every 1/2 cup of peanuts. To find the ratio in terms of cups, we can multiply both sides of the ratio by 2:
3 cups of raisins : 1/2 cup of peanuts --> 6 cups of raisins : 1 cup of peanuts
Therefore, 6 cups of raisins require 1 cup of peanuts. Since we only need 1 cup of raisins in the recipe, we will also need 1/6 cup of peanuts to maintain the ratio.