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.
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:
[tex]\frac{4}{6} = 0.666[/tex] or [tex]\frac{4}{6} = \frac{2}{3}[/tex] (divide both numbers by 2)
Recipe 2:
[tex]\frac{6}{9} = 0.666[/tex] or [tex]\frac{6}{9} = \frac{2}{3}[/tex] (divide both numbers by 3)
Recipe 3:
[tex]\frac{9}{12}[/tex][tex]= 0.75[/tex] or [tex]\frac{9}{12} = \frac{3}{4}[/tex] (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.
