Question

Two of these mixtures taste the same, and one tastes different. Which two recipes will be the same?

a) Recipe 1: 4 cups of orange juice with 6 cups of pineapple juice.
b) Recipe 2: 6 cups of orange juice with 9 cups of pineapple juice.
c) Recipe 3: 9 cups of orange juice with 12 cups of pineapple juice.
c) None of the above

Answer 1

Recipes 1 and 2 will taste the same as they both have the same simplified ratio of orange to pineapple juice, 2:3. Recipe 3 has a different ratio of 3:4 and will taste different.

Step-by-step explanation:

To find out which two recipes will taste the same, we need to compare the ratios of orange juice to pineapple juice in each recipe. The key concept here is to determine if the recipes have the same proportion of ingredients, which can be done by simplifying the ratios. For Recipe 1, the ratio of orange to pineapple juice is 4:6, which simplifies to 2:3 when divided by 2. Recipe 2 has a ratio of 6:9, which also simplifies to 2:3 when divided by 3. Recipe 3 has a ratio of 9:12, which simplifies to 3:4 when divided by 3. Based on the simplified ratios, Recipe 1 and Recipe 2 will taste the same since they both have a ratio of 2:3. Recipe 3 has a different ratio and therefore will taste different.