Final answer:
To find out how many cups of almonds are needed for 12 cups of trail mix, double the original amount required for 6 cups. The answer is 2/3 cup of almonds, which maintains the same ratio of almonds to trail mix.
Step-by-step explanation:
The student is asking how many cups of almonds Mary would need to make 12 cups of trail mix, given that 1/3 cup of almonds is used to make 6 cups of trail mix. To find the answer, we need to set up a proportion because the amount of almonds needed is directly proportional to the amount of trail mix being made. If 1/3 cup of almonds is for 6 cups of trail mix, we know the ratio is 1/3 cup of almonds to 6 cups of trail mix.
For 12 cups of trail mix, we need to maintain the same ratio. Since 12 cups is twice as much as 6 cups, we will need twice as much almonds: 1/3 cup almonds for 6 cups of trail mix is to 2 x 1/3 cup almonds for 2 x 6 cups of trail mix . Therefore, Mary would need 2/3 cup of almonds to make 12 cups of trail mix, which is answer choice a. 2/3 cup.