A recipe for homemade trail mix calls for 1 part dark chocolate, 8 parts dried fruits, and 12 parts nuts. Which of the mixtures below are in a proportional relationship with this blend? Select all that apply.

A. 1.5 oz dark chocolate, 12 oz dried fruit, 18 oz nuts.
B. 2 oz dark chocolate, 16 oz dried fruit, 24 oz nuts.
C. 3 oz dark chocolate, 24 oz dried fruit, 36 oz nuts.
D. 3 oz dark chocolate, 20 oz dried fruit, 36 oz nuts.
E. 4 oz dark chocolate, 30 oz dried fruit, 42 oz nuts.

To determine if the mixtures are in a proportional relationship, we compare the ratios of dark chocolate, dried fruits, and nuts in each mixture. Mixtures B and C are in a proportional relationship with the original blend.

Explanation:

The recipe for homemade trail mix calls for 1 part dark chocolate, 8 parts dried fruits, and 12 parts nuts. To determine if the mixtures are in a proportional relationship, we need to compare the ratios of dark chocolate, dried fruits, and nuts in each mixture. Let's go through each option:

A. 1,5 oz dark chocolate, 12 oz dried fruit, 18 oz nuts. The ratio of dark chocolate to dried fruit is 1:12, and the ratio of dark chocolate to nuts is 1:18. These ratios do not match the original ratio, so this mixture is not in a proportional relationship.

B. 2 oz dark chocolate, 16 oz dried fruit, 24 oz nuts. The ratio of dark chocolate to dried fruit is 2:16, which simplifies to 1:8, matching the original ratio. The ratio of dark chocolate to nuts is 2:24, which simplifies to 1:12, also matching the original ratio. This mixture is in a proportional relationship.

C. 3 oz dark chocolate, 24 oz dried fruit, 36 oz nuts. The ratio of dark chocolate to dried fruit is 3:24, which simplifies to 1:8, matching the original ratio. The ratio of dark chocolate to nuts is 3:36, which simplifies to 1:12, also matching the original ratio. This mixture is in a proportional relationship.

D. 3 oz dark chocolate, 20 oz dried fruit, 36 oz nuts. The ratio of dark chocolate to dried fruit is 3:20, which does not simplify to the original ratio. This mixture is not in a proportional relationship.

E. 4 oz dark chocolate, 30 oz dried fruit, 42 oz nuts. The ratio of dark chocolate to dried fruit is 4:30, which simplifies to 2:15, not matching the original ratio. This mixture is not in a proportional relationship.

Based on the analysis, mixtures B and C are in a proportional relationship with the original blend.

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