Question

The ratios of punch mix to water for several fruit drinks are given. Punch Mix Mix Water Grape 1 cup 3 cups Cherry 5 cups 12 cups Lemon 7 cups 12 cups Orange 2 cups 3 cups Which flavor has the smallest ratio of mix to water?

Answer 1

Answer:

Step-by-step explanation:

We have been given the ratios of punch mix to water for several fruit drinks as : Grape mix (1 cups to 3 cups), Cherry mix (5 cups to 12 cups), Lemon mix (7 cups to 12 cups) and Orange mix (2 cups to 3 cups).

To find which flavor has the smallest ratio of mix to water let us compare all the given proportions by having a common base.  

$\text{Proportion of grape, cherry, lemon and orange mixes to water respectively}=\frac{1}{3} ,\frac{5}{12},\frac{7}{12} ,\frac{2}{3}$  

Now let us have a common denominator 12 as LCM of 3 and 12 is 12.  

$\text{Proportion of grape, cherry, lemon and orange mixes to water respectively}=\frac{1*4}{3*4} ,\frac{5}{12},\frac{7}{12} ,\frac{2*4}{3*4}$

$\text{Proportion of grape, cherry, lemon and orange mixes to water respectively}=\frac{4}{12} ,\frac{5}{12},\frac{7}{12} ,\frac{8}{12}$

We can see that grape mix has the smallest proportion of mix to water, therefore, grape mix will be the correct choice.