The way to know if two recipes will taste the same or not is by checking if the ratio or cups of orange juice to cups of pinneaple juice is the same. To calculate this ratio, we simply divide the number of cups of orange juice by the number of cups of pinneapple juice. If we get the same ratio for different recipes, they taste the same, but if the ratio is different, then the taste is also different. Now, we calculate the ratio for each recipe
Recipe 1: 4 orange juice cups, 6 pinneapple juice cups. Ratio 4/6.
Recipe 2: 6 orange juice cups, 9 pinneapple juice cups. Ratio 6/9.
Recipe 3: 9 orange juice cups, 12 pinneapple juice cups. Ratio 9/12.
Note that for recipe 1:
[tex]\frac{4}{6}=\frac{2\cdot2}{2\cdot3}=\frac{2}{3}[/tex]Also, for recipe 2:
[tex]\frac{6}{9}=\frac{2\cdot3}{3\cdot3}=\frac{2}{3}[/tex]Finally, for recipe 3:
[tex]\frac{9}{12}=\frac{3\cdot3}{3\cdot4}=\frac{3}{4}[/tex]So, since the ratio for recipe 1 is the same as the ratio of recipe 2, then their taste is the same. Recipe 3 has a different taste from recipes 1 and 2.