Question

Here are three different recipes for Orangey-Pineapple Juice. Two of these mixtures taste the same and one tastes different.

Recipe 1: Mix 4 cups of orange juice with 6 cups of pineapple juice.
Recipe 2: Mix 6 cups of orange juice with 9 cups of pineapple juice.
Recipe 3: Mix 9 cups of orange juice with 12 cups of pineapple juice.
Which two recipes will taste the same, and which one will taste different? Explain or show your reasoning.

plz help i have to do like 10 more of these

Answer 1

Answer: Recipe 1 and 2 will taste the same because the ratio of the ingredients is the same, while recipe 3 will taste different because the ratio of ingredients used were different.

Step-by-step explanation:

In this case, the factor that determines whether the mixtures taste the same or different is the ration of ingredients; this is the amount of orange juice added vs the amount of pineapple juice. Here are the ratios for the three recipes:

Recipe 1: 4 to 6 (orange juice to pineapple)

Recipe 2: 6 to 9 (orange juice to pineapple)

Recipe 3: 9 to 12 (orange juice to pineapple)

Now, to compare the ratios these can be written as fractions and then simplified by dividing the numerator into the denominator or reducing the fraction.

Recipe 1:

`(4)/(6) = 0.666` or
`(4)/(6) = (2)/(3)` (divide both numbers by 2)

Recipe 2:

`(6)/(9) = 0.666` or
`(6)/(9) = (2)/(3)` (divide both numbers by 3)

Recipe 3:

`(9)/(12)`
`= 0.75` or
`(9)/(12) = (3)/(4)` (divide both numbers by 3)

This shows recipes 1 and 2 use the same ratio of orange vs pineapple juice (2 to 3), which means the same taste, while the ration in the recipe 3 is different.